Problems and Recent Methods in Operator Theory

This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15-16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17-18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their ``nice'' spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.

Table of Contents:
R. Fleming, From Helgermites to Lipschitz: Remembering Jim Jamison T. Abe, A Mazur-Ulam theorem for normed gyrolinear spaces S. Aryal, H. Choi, and F. Jafari, Sparse Hamburger moment multisequences S. Bandyopadhyay and A. I. Singh, Polynomial representation of quantum entanglement S. Basu, On span of small combination of slices points in Banach spaces F. Botelho and J. Jamison, Surjective isometries on absolutely continuous vector valued function spaces I. Chalendar and J. R. Partington, Compactness, differentiability and similarity to isometry of composition semigroups F. Colonna and M. Tjani, Weighted composition operators from Banach spaces of analytic functions into Bloch-type spaces C. C. Cowen and E. A. Gallardo-Gutierrez, A new proof of a Nordgren, Rosenthal and Wintrobe theorem on universal operators C. Farsi, E. Gillaspy, A. Julien, S. Kang, and J. Packer, Wavelets and spectral triples for fractal representations of Cuntz algebras N. J. Gal, The isometric equivalence problem O. Hatori, Extension of isometries in generalized gyrovector spaces of the positive cones D. Ilisevic, Generalized $n$-circular projections on JB*-triples R. King, Hermitian operators on $H^1_{\mathcal{H}}$ B. Miller, Kernels of adjoints of composition operators with rational symbols of degree two T. Miura and H. Takagi, Surjective isometries on the Banach space of continuously differentiable functions L. Molnar, The arithmetic, geometric and harmonic means in operator algebras and transformations among them B. Randrianantoanina, On sign embeddings and narrow operators on $L_2$ T. S. S. R. K. Rao, Into isometries that preserve finite dimensional structure of the range J. E. Stovall and W. A. Feldman, Associating linear and nonlinear operators D. Thompson, Normality properties of weighted composition operators on $H^2$.