IJPAM: Volume 76, No. 1 (2012)

A DISCUSSION ON THE NATURAL DOMAIN OF
RADIAL TOEPLITZ OPERATORS IN
SEGAL-BARGMANN SPACE

Romina A. Ramırez$^1$, Gerardo L. Rossini$^2$, Marcela Sanmartino$^3$
$^{1,3}$Departamento de Matemática
Facultad de Ciencias Exactas
Universidad Nacional de La Plata
ARGENTINA
$^2$IFLP-CONICET and Departamento de Fısica
Facultad de Ciencias Exactas
Universidad Nacional de La Plata
ARGENTINA


Abstract. We discuss the domain of Toeplitz operators with radial symbols in the Segal-Bargmann space: we point out and correct missleading staments in previous works, establishing the conditions under which a given Toeplitz operator is unitarily equivalent to a diagonal operator in the space $l^{2}(\mathbb{C})$ of square summable complex sequences.

Received: November 11, 2011

AMS Subject Classification: 47B35, 81Q99

Key Words and Phrases: Toeplitz operators, radial symbols

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 1