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Normal Operators on the Banach Space Lp(-∞,∞). Part I

Published online by Cambridge University Press:  20 November 2018

Gregers L. Krabbe
Gregers L. Krabbe*
Affiliation:
Purdue University
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Let be the Boolean algebra of all finite unions of subcells of the plane. Denote by εpthe algebra of all linear bounded transformations of Lp(— ∞, ∞) into itself. Suppose for a moment that p = 2, and let Rp be an involutive abelian subalgebra of εp if Rp is also a Banach space and if Tp ∈ Rp, then:

(i) The family of all homomorphic mappings of into the algebra Rp contains a member EPT such that

(1)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 505 - 518
Copyright
Copyright © Canadian Mathematical Society 1961

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