Weighted composition operators on weighted Lorentz spaces

Eryilmaz, Ilker

doi:10.4064/cm128-2-1

Cited by 2 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They also play an important role in the study of operators on Hilbert spaces. Consequently, by now there exists a vast literature on the properties of these transformations in various function spaces; we refer the interested reader to the beautiful books [5,35,36], and, for more recent studies, to [9][10][11]14,23,25], for instance.…”

Section: Introductionmentioning

confidence: 99%

Basic properties of multiplication and composition operators between distinct Orlicz spaces

et al. 2016

View full text Add to dashboard Cite

First, we present some simple (and easily verifiable) necessary conditions and sufficient conditions for boundedness of the multiplication operator M u and composition operator C T acting from Orlicz space L 1 () into Orlicz space L 2 () over arbitrary complete, σ-finite measure space (, , μ). Next, we investigate the problem of conditions on the generating Young functions, the function u, and/or the function h = d(μ • T −1)/dμ, under which the operators M u and C T are of closed range or finite rank. Finally, we give necessary and sufficient conditions for boundedness of the operators M u and C T in terms of techniques developed within the theory of Musielak-Orlicz spaces.

show abstract

Section: Introductionmentioning

confidence: 99%

Basic properties of multiplication and composition operators between distinct Orlicz spaces

et al. 2016

View full text Add to dashboard Cite

show abstract

Composition Operators between BC-rearrangement Invariant BC-Module Spaces

Eryilmaz

2024

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

This paper investigates the behavior and structural properties of composition operators within the framework of 𝔹ℂ-rearrangement 𝔹ℂ-module spaces. Building upon the foundational concepts of 𝔹ℂ-modules and rearrangement-invariant spaces, we explore the intricate interplay between these spaces under the action of composition operators. Our study delves into the algebraic and topological aspects of composition operators, elucidating their impact on the underlying space structures. After establishing the necessary background on 𝔹ℂ -modules and 𝔹ℂ-rearrangement-invariant spaces and laying the groundwork for our subsequent analysis, a rigorous examination of composition operators, we uncover fundamental properties such as 𝔻-continuity, 𝔻- boundedness, and 𝔻-compactness, shedding light on the intrinsic characteristics of these operators within 𝔹ℂmodule spaces.

show abstract

Weighted composition operators on weighted Lorentz spaces

Abstract: The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p, q, wdµ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.

Cited by 2 publications

References 10 publications

Basic properties of multiplication and composition operators between distinct Orlicz spaces

Basic properties of multiplication and composition operators between distinct Orlicz spaces

Composition Operators between BC-rearrangement Invariant BC-Module Spaces

Contact Info

Product

Resources

About