Trends in Banach Spaces and Operator Theory: A Conference on Trends in Banach Spaces and Operator Theory, October 5-9, 2001, University of Memphis

This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L_p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.

Table of Contents:
Characterizations of the reflexive spaces in the spirit of James' Theorem by M. D. Acosta, J. B. Guerrero, and M. R. Galan Uniqueness of unconditional bases in quasi-Banach spaces by F. Albiac, N. J. Kalton, and C. Leranoz A note on the method of minimal vectors by G. Androulakis The projective tensor product I by J. Diestel, J. Fourie, and J. Swart Spectrum of a weakly hypercyclic operator meets the unit circle by S. J. Dilworth and V. G. Troitsky The dynamics of cohyponormal operators by N. S. Feldman Hilbert-Schmidt composition operators on Dirichlet spaces by E. A. Gallardo-Gutierrez and M. J. Gonzalez A remark on sectorial operators with an $H^{\infty}-$ calculus by N. J. Kalton Borel injective tensor product and convolution of vector measures and their weak convergence by J. Kawabe On linear operator pencils and inclusions of images of balls by V. A. Khatskevich and V. S. Shulman Ordinal indices and $\ell^1$-spreading models by D. H. Leung and W.-K. Tang Characterizing the existence of local Smith forms for $\mathcal{C}^\infty$ families of matrix operators by J. Lopez-Gomez and C. Mora-Corral Convex geometry of Coxeter-invariant polyhedra by N. McCarthy, D. Ogilvie, N. Zobin, and V. Zobin Commutators on bounded symmetric domains in $\mathbb{C}^n$ by J. Miao Growth conditions and decomposable extensions by T. L. Miller, V. G. Miller, and M. M. Neumann Differences of composition operators by J. Moorhouse and C. Toews Complex vs real variables for real 3-homogeneous polynomials on $\ell_1^2$: A counterexample by G. A. Munoz The Fourier-Stieltjes and Fourier algebras for locally compact groupoids by A. L. T. Paterson Preserving the commutant under functional calculus by G. T. Prajitura $L_p$-spaces associated with a von Neumann algebra without trace: a gentle introduction via complex interpolation by Y. Raynaud Banach and operator space structure of $C^*$-algebras by H. P. Rosenthal How many operators exist on a Banach space? by T. Schlumprecht Maximal algebra norms by G. V. Wood On Banach spaces with small spaces of operators by A. Zsak A remark on $p$-summing norms of operators by A. Zvavitch.