# A Functional Calculus for Quotient Bounded Operators

Research paper by Mirel Sorin Stoian

Indexed on: 16 Mar '07Published on: 16 Mar '07Published in: Mathematics - Functional Analysis

#### Abstract

If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on X. The classic functional calculus for the bounded operators on Banach space is generalized for such bounded operators. Also are studied some spectral propreties of the locally bounded operators.