IJPAM: Volume 54, No. 3 (2009)

AN INTEGRAL REPRESENTATION FOR
GENERAL OPERATORS IN BANACH SPACES

Alexandra Cojuhari$^1$, Jerzy Stochel$^2$
$^{1,2}$Department of Applied Mathematics
AGH University of Science and Technology
30, Al. Mickiewicza, Cracow, 30-059, POLAND
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Results concerning spectral sets in von Neumann's sense are extended to operators on Banach spaces. In particular, there are generalized well-known Lebow's results concerning measure-theoretic characterization of spectral sets. Applications to harmonic spectral measures are also considered.

Received: July 7, 2009

AMS Subject Classification: 46G10, 47A25, 47A67

Key Words and Phrases: operator-valued measures and integration, integral representation, functional calculus, spectral sets

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3