Normal-equivalent operators and operators with dual of scalar-type

Authors
Ghaemi, MB
Citation
Mb. Ghaemi, Normal-equivalent operators and operators with dual of scalar-type, P EDIN MATH, 43, 2000, pp. 261-268
Citations number
11
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
ISSN journal
00130915 → ACNP
Volume
43
Year of publication
2000
Part
2
Pages
261 - 268
Database
ISI
SICI code
0013-0915(200006)43:<261:NOAOWD>2.0.ZU;2-I
Abstract
If T is an element of L(X) is such that T' is a scalar-type prespectral ope rator, then ReT' and ImT' are both dual operators. It is showm that that th e possession of a functional calculus for the continuous functions on the s pectrum of T is equivalent to Tl being scalar-type prespectral of class X, thus answering a question of Berkson and Gillespie.