One-sided M-Ideals and multipliers in operator spaces, I
| Autor: | Vrej Zarikian, Edward G. Effros, David P. Blecher |
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| Rok vydání: | 2002 |
| Předmět: |
Discrete mathematics
General Mathematics Mathematics - Operator Algebras Primary 46L07 Secondary 46L08 Finite-rank operator Operator theory Compact operator Functional Analysis (math.FA) Mathematics - Functional Analysis Multiplier (Fourier analysis) Pseudo-monotone operator symbols.namesake Von Neumann's theorem Operator algebra Von Neumann algebra FOS: Mathematics symbols Operator Algebras (math.OA) Mathematics |
| Zdroj: | Pacific Journal of Mathematics. 206:287-319 |
| ISSN: | 0030-8730 |
| DOI: | 10.2140/pjm.2002.206.287 |
| Popis: | The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is an operator A--B-bimodule for $C^{*}$-algebras A and B, then the module operations on X are automatically weak$^{*}$ continuous. One sided L-projections are introduced, and analogues of various results from the classical theory are proved. An assortment of examples is considered. |
| Databáze: | OpenAIRE |
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