Linear and Multilinear Algebra and Function Spaces.

Cover -- Title page -- Contents -- Preface -- Biduality in weighted spaces of analytic functions -- Introduction -- 1. New solutions to the Biduality Problem -- 2. Density of norm-attaining functions in ℋᵥ( ) -- Acknowledgement -- References -- Interpolation with functions in the analytic Wiener algebra -- 1. Introduction -- 2. Main results -- 3. Technical tools -- 4. Λ-Carleson sets -- 5. Interpolating sets -- References -- Jordan isomorphisms as preservers -- 1. Introduction -- 2. Linear preserver characterizations of Jordan *-isomorphisms between *-algebras -- 3. Non-linear characterizations of Jordan *-isomorphisms on the self-adjoint and positive definite parts of *-algebras -- 4. Additional non-linear characterizations on the self-adjoint and positive definite parts of the full operator algebra ( ) -- References -- Multiplicatively pseudo spectrum-preserving maps -- 1. Introduction -- 2. Main results -- 3. Preliminaries -- 4. Proof of Theorem 2.1 -- 5. Proof of Theorem 2.3 -- 6. Concluding remarks -- References -- On algebraic characterizations of advertibly complete algebras -- 1. Introduction -- 2. Preliminaries -- 3. Characterizations of advertible completeness for general topological algebras -- 4. Characterizations of advertible completeness for GB*-algebras -- References -- Polar decomposition, Aluthge and mean transforms -- 1. Introduction -- 2. Polar decomposition of bounded linear operators on a Hilbert space -- 3. Aluthge transform -- 4. Mean transform -- 5. Mean transform and Schatten -ideals -- 6. Open questions -- References -- Recent progress on local spectrum-preserving maps -- 1. Introduction -- 2. Background from local spectral theory -- 3. Multiplicatively spectrum preserving maps -- 4. Linear maps preserving the local spectrum -- 5. Product and nonlinear local spectra preservers.

6. Triple product and nonlinear local spectra preservers -- 7. Jordan product and nonlinear local spectra preservers -- 8. Lie product and nonlinear local spectra preservers -- 9. Concluding remarks and open problems -- References -- Sadovskii-type fixed point results for edge-preserving mappings -- 1. Introduction -- 2. Notations and preliminaries -- 3. Fixed points of condensing mappings on a metric space with a monotone distance graph -- Acknowledgements -- References -- The joint numerical radius on *-algebras -- 1. Introduction and preliminaries -- 2. Statement of the main results. -- 3. Proof of theorem 2.1 -- 4. Proof of theorem 2.3 -- 5. Proof of theorem 2.5 -- 6. Concluding remarks. -- References -- Weighted composition operators on non locally convex weighted spaces with operator-valued weights -- Introduction -- 1. Preliminaries -- 2. Completeness of ( , ) and ₀( , ) -- 3. Continuous weighted composition operators -- 4. Bounded weighted composition operators -- 5. Locally equicontinuous weighted composition operators -- References -- Zero product preserving maps on matrix rings over division rings -- 1. Introduction -- 2. Preliminaries -- 3. The general case -- 4. The case where is continuous -- 5. The case where is additive -- References -- Back Cover.

This volume contains the proceedings of the International Conference on Algebra and Related Topics, held from July 2-5, 2018, at Mohammed V University, Rabat, Morocco. Linear reserver problems demand the characterization of linear maps between algebras that leave invariant certain properties or certain subsets or relations. One of the most intractable unsolved problems is Kaplansky's conjecture: every surjective unital invertibility preserving linear map between two semisimple Banach algebras is a Jordan homomorphism. Recently, there has been an upsurge of interest in nonlinear preservers, where the maps studied are no longer assumed linear but instead a weak algebraic condition is somehow involved through the preserving property. This volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on C^*-algebras, advertible complete algebras, and Gelfand-Mazur algebras. The volume also contains a survey on recent progress on local spectrum-preserving maps. Several articles in the volume present results about weighted spaces and algebras of holomorphic or harmonic functions, including biduality in weighted spaces of analytic functions, interpolation in the analytic Wiener algebra, and weighted composition operators on non-locally convex weighted spaces.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.