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The Geometry and Norm-Attainability of Operators in Operator Ideals: The Role of Singular Values and Compactness

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Publication Date
2024-12-31
Author
Mogoi, N. Evans
Obogi, Robert
Type
Article
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Abstract/Overview

This paper investigates the geometry and norm-attainability of operators within various operator ideals, with a particular focus on the role of singular values and compactness. We explore the behavior of norm-attainable operators in the context of classical operator ideals, such as trace-class and Hilbert-Schmidt operators, and examine how their geometric and algebraic properties are influenced by membership in these ideals. A key result of this study is the connection between the singular values of trace-class operators and their operator norm, establishing a foundational relationship for understanding norm-attainment. Additionally, we explore the conditions under which weakly compact and compact operators can attain their operator norm, providing further insights into the structural properties that govern norm-attainability in operator theory. The findings contribute to a deeper understanding of the interplay between operator ideals and norm-attainability, with potential applications in functional analysis and related fields.

Subject/Keywords
Norm-Attainability; Operator Ideals; Singular Values; Trace-Class Operator
Publisher
Open Journal of Mathematical Analysis
Permalink
http://ir.jooust.ac.ke/handle/123456789/14229
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