Positive Operators and Semigroups on Banach Lattices
Positive Operators and Semigroups on Banach Lattices

Author: C.B. Huijsmans

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 151

ISBN-13: 940172721X

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During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators. In particular, the recent investigations in the structure of the lattice ordered (Banach) algebra of the order bounded operators of a Banach lattice have led to many important results in the spectral theory of positive operators. The contributions contained in this volume were presented as lectures at a conference organized by the Caribbean Mathematics Foundation, and provide an overview of the present state of development of various areas of the theory of positive operators and their spectral properties. This book will be of interest to analysts whose work involves positive matrices and positive operators.

Banach Spaces with a Unique Unconditional Basis, up to Permutation
Banach Spaces with a Unique Unconditional Basis, up to Permutation

Author: Jean Bourgain

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 119

ISBN-13: 082182323X

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In the memoir we examine the question which Banach spaces have a unique unconditional basis, up to equivalence and permutation. We solve this question for some infinite direct sums of classical sequence spaces and for a Tsirelson type space. We also classify, up to isomorphism, all the complemented subspaces of some of the examples mentioned above.