Function Spaces

This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L^p$-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented.

Table of Contents:
Components of resolvent sets and local spectral theory by P. Aiena and F. Villafane The Fejer-Riesz inequality and the index of the shift by J. R. Akeroyd A Cauchy-Green formula on the unit sphere in $\mathbf{C}^2$ by J. T. Anderson and J. Wermer On $\alpha$-dual algebras by H. Arizmendi, A. Carrillo, and L. Palacios A connected metric space that is not separably connected by R. M. Aron and M. Maestre Weighted Chebyshev centres and intersection properties of balls in Banach spaces by P. Bandyopadhyay and S. Dutta The boundary of the unit ball in $H^1$-type spaces by P. Beneker and J. Wiegerinck Complete isometries - an illustration of noncommutative functional analysis by D. P. Blecher and D. M. Hay Some recent trends and advances in certain lattice ordered algebras by K. Boulabiar, G. Buskes, and A. Triki An extension of a theorem of Wermer, Bernard, Sidney and Hatori to algebras of functions on locally compact spaces by E. Briem Some mapping properties of $p$-summing operators with Hilbertian domain by Q. Bu The unique decomposition property and the Banach-Stone theorem by A. Cumock, J. Howroyd, and N.-C. Wong A survey of algebraic extensions of commutative, unital normed algebras by T. Dawson Some more examples of subsets of $c_0$ and $L^1[0,1]$ failing the fixed point property by P. N. Dowling, C. J. Lennard, and B. Turett Homotopic composition operators on $H^\infty(B^n)$ by P. Gorkin, R. Mortini, and D. Suarez Characterization of conditional expectation in terms of positive projections by J. J. Grobler and M. De Kock The Krull nature of locally $C^*$-algebras by M. Haralampidou Characterizations and automatic linearity for ring homomorphisms on algebras of functions by O. Hatori, T. Ishii, T. Miura, and S.-E. Takahasi Carleson embeddings for weighted Bergman spaces by H. Jarchow and U. Kollbrunner Weak$^{\ast}$-extreme points of injective tensor product spaces by K. Jarosz and T. S. S. R. Rao Determining sets and fixed points for holomorphic endomorphisms by K.-T. Kim and S. G. Krantz Localization in the spectral theory of operators on Banach spaces by T. L. Miller, V. G. Miller, and M. M. Neumann Abstract harmonic analysis, homological algebra, and operator spaces by V. Runde Relative tensor products for modules over von Neumann algebras by D. Sherman Uniform algebras generated by unimodular functions by S. J. Sidney Analytic functions on compact groups and their applications to almost periodic functions by T. Tonev and S. A. Grigoryan.