C*-algebra generated by horizontal Toeplitz operators on the Fock space
| Autor: | Kevin Esmeral, Nikolai Vasilevski |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Dense set General Mathematics 010102 general mathematics 01 natural sciences Toeplitz matrix Fock space Algebra Uniform continuity Multiplication operator Bounded function 0103 physical sciences 010307 mathematical physics 0101 mathematics Invariant (mathematics) Mathematics Toeplitz operator |
| Zdroj: | Boletín de la Sociedad Matemática Mexicana. 22:567-582 |
| ISSN: | 2296-4495 1405-213X |
| Popis: | We introduce the so-called horizontal Toeplitz operators acting on the Fock space and give an explicit description of the C*-algebra generated by them. We show that any Toeplitz operator with $$L_{\infty }$$ -symbol, which is invariant under imaginary translations, is unitarily equivalent to the multiplication operator by its “spectral function”. This result is also true for the Toeplitz operators whose defining symbols are invariant under translations over any Lagrangian plane. The main result of the paper states that the corresponding spectral functions form a dense subset in the C*-algebra of bounded uniformly continuous functions with respect to the standard metric on $$\mathbb {R}^{n}$$ . |
| Databáze: | OpenAIRE |
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