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Symbolic calculus of operators with unit numerical radius

✍ Scribed by S.W. Drury

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
119 KB
Volume
428
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let T be a linear operator on a complex Hilbert space with numerical radius bounded by one. We study the norm and numerical range of p(T ) where p is a disk algebra function satisfying sup |z| 1 |p(z)| 1 and p(0) is known. As corollaries we are able to establish for p an arbitrary complex polynomial the known estimate due to Okubo and AndΓ΄ p(T ) 2 sup |z| 1 |p(z)| for the operator norm and the estimate w(p(T )) 5 4 sup |z| 1 |p(z)|

for the numerical radius.

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