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1
Content available remote Solvability of new (SSIE) involving the continuous and residual spectra of the generalized difference operator B (r, s) on c0
Malafosse Bruno de
Fasciculi Mathematici
|
2023
|
nr 66
61--75
EN
Let U+ be the set of all positive sequences. Then, given any sequence z = (zn)n≥1 ∈ U+ and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n≥1 such that y/z = (yn/zn)n≥1 ∈ E. We use the notation sz = (ℓ∞)z. In this paper, for given r, s≠ 0 and for every λ ∈ ℂ, we determine the set of all positive sequences x = (xn)n≥1 that satisfy the (SSIE) with an operator (c0)B(r,s)−λI ⊂ Ɛ + sx, where Ɛ ⊂ sθ for some θ ∈ U+ is a linear space of sequences, in each of the cases, (1) |λ - r| > |s|, or λ = r, (2) |λ - r| = |s| and (3) |λ - r| < |s| and λ ≠ r. These cases are associated with the continuous and residual spectra σc (B (r, s), c0) and σr (B (r, s), c0), of B (r, s) on c0, determined by Altay and Başar in [2]. We apply these results to the solvability of the (SSIE) (c0)B(r,s)−λI ⊂ s(c)R +sx for all λ ∈ ℂ and R > 0. Then we deal with the (SSIE) (c0)Δ−λI ⊂ bvp + sx and (c0)B(r,s)−λI ⊂ ERɑ + sx, for E = c0, c, or ℓ∞, where Rɑ, ɑ ∈ U+, is the Rhaly matrix. These results extend those stated in [21].
2
Content available On the analytic α-Lipschitz vector-valued operators
Shokri Abbasali
Journal of Mathematics and Applications
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2022
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Vol. 45
181--190
EN
Let (X, d) be a non-empty compact metric space in C, (B, ∥ . ∥) be a commutative unital Banach algebra over the scalar field F(= R or C) and α ∈ R with 0 < α ≤ 1. In this work, first we define the analytic α-Lipschitz B-valued operators on X and denote the Banach algebra of all these operators by Lipα A(X, B). When B = F, we write Lipα A(X) instead of Lipα A(X, B). Then we study some interesting results about Lipα A(X, B), including the relationship between Lipα A(X, B) with Lipα A(X) and B, and also characterize the characters on Lipα A(X, B).
3
Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
Saha Dipankar, Sen Mausumi, Roy Santanu
Journal of Applied Analysis
|
2022
|
Vol. 28, nr 2
199--210
EN
This paper signifies the beauty of fixed point theory in the context of attaining the sufficient condition for the existence of the solution of a non-linear functional-integral equation in an unbounded interval. Here a non-linear integral equation (NLIE) involving a fractional operator is taken in the form of an operator equation. Utilizing the perception of measure of noncompactness (MNC) along with certain relevant assumptions, it is proved that the operator equation satisfies the Darbo condition for the product of operators in a Banach algebra. Finally, the result obtained is verified by the assistance of the numerical example.
4
Content available remote Corona theorem for strictly pseudoconvex domains
Gwizdek Sebastian
Opuscula Mathematica
|
2021
|
Vol. 41, no. 6
843--848
EN
Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved “abstract” Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries
5
Content available Description of the scattering data for Sturm-Liouville operators on the half-line
Mykytyuk Yaroslav, Sushchyk Natalia
Opuscula Mathematica
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2019
|
Vol. 39, no. 4
557--576
EN
We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to [formula], where [formula] is a monotonically nondecreasing function from some family R. In particular, R includes the functions [formula]
6
Content available On some fixed point theorems for expansive mappings in dislocated cone metric spaces with Banach algebras
Auwalu Abba, Hinçal Evren, Mishra Lakshmi Narayan
Journal of Mathematics and Applications
|
2019
|
Vol. 42
21--33
EN
In this paper, we introduced the notion of generalized expansive mappings in dislocated cone metric spaces with Banach algebras. Furthermore, we prove some fixed point theorems for generalized expansive mappings in dislocated cone metric spaces with Banach algebras without the assumption of normality of cones. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of many recent results in the literature.
7
Content available remote Derivations into annihilators of the ideals of Banach algebras
Teymouri Akram, Bodaghi Abasalt, Bagha Davood Ebrahimi
Demonstratio Mathematica
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2019
|
Vol. 52, nr 1
20--28
EN
In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with Ј-weak amenability and ideal amenability, where Ј is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/Ј-weak amenability and of Ј-weak amenabilitydo not coincide for Banach algebras in general.
8
Content available Inverse scattering problems for half-line Schrödinger operators and Banach algebras
Mykytyuk Y., Sushchyk N.
Opuscula Mathematica
|
2018
|
Vol. 38, no. 5
719--731
EN
The inverse scattering problem for half-line Schrodinger operators with potentials from the Marchenko class is shown to be closely related to some Banach algebra of functions on the line. In particular, it is proved that the topological conditions in the Marchenko theorem can be replaced by the condition that the scattering function should belong to this Banach algebra.
9
Content available Measures of noncompactness in a Banach algebra and their applications
Dudek S.
Journal of Mathematics and Applications
|
2017
|
Vol. 40
69--84
EN
In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.
10
Content available remote Closed ideals in a new class of algebras of holomorphic functions on the disc
Merino-Cruz H., Wawrzyńczyk A.
Commentationes Mathematicae
|
2014
|
Vol 54, No. 1
29--37
EN
We define a new class of Banach algebras of holomorphic functions on the unit disc D which contains the algebras studied in [GMR2] and [GW]. To a function G of the class A1(D) nowhere vanishing in D we associate a Banach algebra AnG(D) contained in the disc algebra A(D). We prove that all closed ideals of AnG(D) of at most countable hull are of the standard form.
11
Content available remote Maximal ideal space of certain α-Lipschitz operator algebras
Shokri A. A., Shokri A.
Journal of Mathematics and Applications
|
2012
|
Vol. 35
83--89
EN
In a recent paper by A. Ebadian and A.A. Shokri [1], a α-Lipschitz operator from a compact metric space X into a unital bounded commutative Banach algebra B is defined. Let (X,d) be a nonempty compact metric space, 0<α≤1 and (B, || . ||) be a unital bounded commutative Banach algebra. Let Lipα(X,B) be the algebra of all bounded continuous operators ƒ: X → B such that [formula/wzor]. In this work, we characterize the maximal ideal space of Lipα(X,B).
12
Content available remote Ditkin's condition and ideals with at most countable hull in algebras of functions analytic in the unit disc
Sołtysiak A., Wawrzyńczyk A.
Commentationes Mathematicae
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2012
|
Vol. 52, [Z] 1
101-112
13
Content available remote On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense
Ereu T., Merentes N., Rzepka B., Sanchez J. L.
Journal of Mathematics and Applications
|
2010
|
Vol. 33
35-50
EN
In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.
14
Content available remote Functions of two variables with bounded φ-variation in the sense of Riesz
Aziz W., Leiva H., Merentes N., Sánchez J. L.
Journal of Mathematics and Applications
|
2010
|
Vol. 32
5-23
EN
In this paper we introduce the concept of bounded φ- variation function, in the sense of Riesz, dened in a rectangle [wzór]. We prove that the linear space [wzór] generated by the class [wzór] of all φ-bounded variation functions is a Banach algebra. Moreover, we give necessary and sucient conditions for the Nemytskii operator acting in the space [wzór] to be globally Lipschitz.
15
Content available remote Some inequalities for the maximum of the spectrum for the real part of two operators product in Hilbert spaces
Dragomir S. S.
Demonstratio Mathematica
|
2010
|
Vol. 43, nr 3
665-680
EN
Some inequalities for the maximum and the minimum of the spectrum for the real part of a product of two operators in Hilbert spaces are given. Applications for one operator whose transform C(...) (introduced by the author in [9]) is accretive, are given as well.
16
Content available remote Some remarks on the algebra of functions of two variables with bounded total Φ-variation in Schramm sense
Ereu T., Merentes N., Sánchez J-L.
Commentationes Mathematicae
|
2010
|
Vol. 50, [Z] 1
23-33
EN
This paper is devoted to discuss some generalizations of the bounded total Φ-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total Φ-variation in Schramm sense has the structure of a Banach algebra.
17
Content available remote Spectra of the operator of the first difference in salpha, s)/alpha and lp (alpha) (1
Fares A., Malafosse B.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 3
661-676
EN
In this paper we deal with the spectrum of the operator of the first difference A considered as an operator from E to itself where E is one of the sets [...].We apply these results to characterize matrix transformations mapping in E [...] or N. This paper generalizes some results given in [8] and [3].
18
Content available remote Pairs of derivations on rings and Banach algebras
Wei F., Xiao Z.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 2
297-308
EN
We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.
19
Content available remote An identity with derivations on rings and Banach algebras
Fosner A., Fosner M., Vukman J.
Demonstratio Mathematica
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2008
|
Vol. 41, nr 3
525-530
20
Content available remote A note Gateaux differentials of hermitian elements in Banach algebras
Herzog G., Schmoeger C.
Demonstratio Mathematica
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2008
|
Vol. 41, nr 4
909-913
EN
Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.
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