Linear and Multilinear Algebra and Function Spaces: International Conference Algebra and Related Topics (Icart 2018) July 2-5, 2018 Mohammed V University , Rabat, Morocco (Contemporary Mathematics)

The International Conference on Algebra and Related Topics (ICART 2018)was held at Faculty of Sciences, Mohammed V University in Rabat, Morocco, fromJuly 2 to 5, 2018. It covered various research areas presented in three parallelsessions. “Linear and Multilinear Algebra, and Function spaces (in short LMAFS)”was one of them. The topics of interest of this session included linear and nonlinearpreserver problems, Banach algebras, topological algebras, operator theory, andweighted function spaces. Numerous international experts in these areas presentedtheir ongoing research, and interacted with their colleagues and Ph.D studentsworking in their fields.Linear preserver problems demand the characterization of linear maps betweenalgebras that leave invariant certain properties or subsets or relations. The earliestresult on linear preserver problems was established by Frobenius in 1896. Frobeniuscharacterized all bijective linear transformations on the algebra Mn(C) of complexmatrices that preserve the determinant of matrices. His result was generalized in1925 by Schur for subdeterminants of a fixed order and in 1949 by Dieudonn ́e toarbitrary fields and for linear maps preserving the set of singular matrices. Sincethen, various linear preserver problems have been considered and a number oftechniques have been developed to treat them. One of the most intractable unsolvedproblems in this active research area is the famous Kaplansky’s conjecture thatasserts that every surjective unital invertibility preserving linear map between twosemisimple Banach algebras is a Jordan homomorphism. This conjecture has notbeen fully solved yet and remains open even for general C∗-algebras, but it hasbeen confirmed, in particular, for von Neumann algebras and for the algebra of allbounded linear operators on a Banach space. 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(U) 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 C*-algebras 3. Non-linear characterizations of Jordan *-isomorphisms on the self-adjoint and positive definite parts of C*-algebras 4. Additional non-linear characterizations on the self-adjoint and positive definite parts of the full operator algebra B(H) 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 p-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 C*-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 CV(X,A) and CV0(X,A) 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 φ is continuous 5. The case where φ 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 in 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. 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 ∗ 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. Contains the proceedings of the International Conference on Algebra and Related Topics, held in July 2018, in Rabat, Morocco. The volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on $C^*$-algebras, and advertible complete algebras.