Extensions of semigroups of operators

Journal article

Let T be a representation of an abelian semigroup S on a Banach space X. We identify a necessary and sufficient condition, which we name superexpansiveness, for T to have an extension to a representation U on a Danach space Y containing X such that each U(t) (t ∈ S) has a contractive inverse. Although there are many such extensions (Y, U) in general, there is a unique one which has a certain universal property. The spectrum of this extension coincides with the unitary part of the spectrum of T, so various results in spectral theory of group representations can be extended to superexpansive representations.

Authors: Batty, C; Yeates, S

• Publication status: Published
• Journal: JOURNAL OF OPERATOR THEORY
• Volume: 46
• Issue: 1
• Pages: 139-157
• Publication date: 2001-01-01
• ISSN: 0379-4024
• Language: English
• Keywords: approximate eigenvalue; extension; expansive; representation; unitary spectrum; superreflexive; generic; isometry; semigroup