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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 remote On generalized Orlicz sequence spaces defined by double sequences
Kolk E.
Fasciculi Mathematici
|
2015
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Nr 55
65--80
EN
S.D. Parashar and B. Choudhary defined in 1994 certain paranorms for some Orlicz sequence spaces. Their ideas are applied later for topologization of various generalized Orlicz sequence spaces. The author determines in 2011 some alternative F-seminorms (which are also paranorms) for such spaces. In this paper these results are extended to generalized Orlicz sequence spaces defined via double sequences.
3
Duals of homogeneous weighted sequence Besov spaces and applications
Huang P.-K., Wang K.
Journal of Applied Analysis
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2011
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Vol. 17, nr 2
181-205
EN
In this article, we study the duals of homogeneous weighted sequence Besov spaces b α,q p,w, where the weight w is non-negative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence spaces which characterize the duals of b α,q p,w. Also, we find the necessary and sufficient conditions for the boundedness of diagonal matrices acting on homogeneous weighted sequence Besov spaces. Using these results, we give some applications to characterize the boundedness of Fourier-Haar multipliers and paraproduct operators. In this situation, we need to require that the weight w is an Ap weight.
4
Content available remote Certain spaces of sequences of fuzzy numbers defined by a modulus function
Talo O., Basar F.
Demonstratio Mathematica
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2010
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Vol. 43, nr 1
139-149
EN
The main purpose of the present paper is to introduce the spaces l infinity (F, f), c(F, f), co(F, f) and lp(F, f, s) of sequences of fuzzy numbers defined by a modulus function. Furthermore, some inclusion theorems related to these sets are given and shown that l infinity(Ff), co F,f) and Lp(FJ,s) are solid.
5
Content available remote On a new sequence space related to the Orlicz sequence space
Khan V. A.
Journal of Mathematics and Applications
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2008
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Vol. 30
61-69
EN
The space m(Φ) was introduced by sargent[14]and further studied by Malkowsky and Mursaleen [8] and Mursaleen [9]. In this paper we extend this space to m(M, Φ, p) and study some of its properties, inclusions relations and its relation with the Orlicz sequence space l(sub M).
6
Content available remote Strong invariant A-summability with respect to a sequence of modulus functions in seminormed space
Bhardwaj V., Bala I.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
869-877
EN
The object of this paper is to introduce some new strongly invariant A-summable sequence spaces defined by a sequence of modulus functions T = (fk) in a seminormed space, when A = (ank) is a non-negative regular matrix. Various algebraic and topological properties of these spaces, and some inclusion relations between these spaces have been discussed. Finally, we study some relations between ^4-invariant statisti-cal convergence and strong invariant A-summability with respect to a seąuence of modulus functions in a seminormed space.
7
Content available remote Boundedness of superposition operators on some sequence spaces defined by moduli
Molder A.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 4
869-886
EN
For a solid sequence space lambda and a sequence of modulus functions fi = (phik) let lambda(fi) = {x = (xk) : (phik(|xk|)) is an element of lambda}. Provided another solid sequence space ž and a sequence of modulus functions psi= psi(k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators Pf from lambda(fi)) into ž(psi) for some Banach sequence spaces lambda and ž under the assumptions that topologies on the sequence spaces lambda(fi) and ž(psi) are given by certain F-norms. As applications we characterize bounded superposition operators on some multiplier sequence spaces of Maddox type.
8
Content available remote Vector-valued FK-spaces defined by a modulus function
Yilmaz Y., Solak I.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
633--640
EN
We introduced and investigated the sequence space lambda (Xk,r,f,s) defined by a modulus function f, and constructed its FK-structure under some conditions. Also we exposed some inclusion relations among the variations of the space.
9
Content available remote Superposition operators on sequence spaces defined by (phi)-functions
Kolk E.
Demonstratio Mathematica
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2004
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Vol. 37, nr 1
159--175
10
Content available remote Some sequence spaces defined by Orlicz functions
Bhardwaj V., Singh N.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
571-582
EN
The object of this paper is to introduce a new concept of lacunary strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We establish some elementary connections between lacunary strong convergence and lacunary strong convergence with respect to an Orlicz function which satisfies l2-condition. It is also shown that if a sequence is lacunary strongly convergent with respect to an Orlicz function then it is lacunary statistically convergent. In addition, lacunary strong convergence with respect to an Orlicz function is compared to other summability methods.
11
Content available remote Musielak-Orlicz spaces of sequences connected with strong summability
Waszak A., Żurakowski D.
Fasciculi Mathematici
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1998
|
Nr 28
157-165
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