Surveys in Mathematics and its Applications

ISSN 1842-6298
 Volume 1 (2006), 61 - 69

A FUNCTIONAL CALCULUS FOR QUOTIENT BOUNDED OPERATORS

Sorin Mirel Stoian

Abstract. If (X, P) is a sequentially locally convex space, then a quotient bounded operator T beloging to QP is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of algebra QP. The classic functional calculus for bounded operators on Banach space is generalized for bounded elements of algebra QP.

2000 Mathematics Subject Classification: 47A60, 46A03.
Keywords: locally convex space, functional calculus.

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Acknowledgement. This work was supported by the CEEX grant ET65/2005, contract no 2987/11.10.2005, from the Romanian Ministry of Education and Research.

Sorin Mirel Stoian
University of Petroşani,
Faculty of Sciences, Department of Mathematics,
Str. Universităţii, Nr. 20, Petroşani,
Romania.
e-mail: mstoian@upet.ro

http://www.utgjiu.ro/math/sma