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Characterizations of compact operators on ℓp-type fractional sets of sequences

Özger Faruk

Demonstratio Mathematica

2019

Vol. 52, nr 1

105--115

Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp-type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.

Compactness result and its applications in integral equations

Krukowski M., Przeradzki B.

Journal of Applied Analysis

2016

Vol. 22, nr 2

153--161

A version of the Arzelà–Ascoli theorem for X being a σ-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem.

Multiplication operators on Cesàro sequence spaces

Komal B. S., Pandoh S., Raj K.

Demonstratio Mathematica

2016

Vol. 49, nr 4

430--436

In this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces.

Remarks on the spectrum of a compact convex set of compact operators

Pham K. A., Nguyen X. T.

Journal of Applied Analysis

2010

Vol. 16, nr 2

259-264

In this note we derive a necessary and sufficient condition for a compact convex set of linear compact operators acting in a complex Hilbert space to have the spectrum outside a prescribed closed convex subset of the complex plane.

Complemented spaces of operators

Bator E. M., Lewis P. W.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 4

413-416

The complementation of various classes of operators in the space L(E, F) of bounded linear operators between Banach spaces E and F is studied.

Cesaro conull FK-spaces

Ince H.

Demonstratio Mathematica

2000

Vol. 33, nr 1

109-121

The purpose of this paper is to study the (strongly) Cesaro conull FK-spaces and to give some characterizations.