Counterexamples concerning powers of sectorial operators on a Hilbert space
1999 ◽
Vol 60
(3)
◽
pp. 459-468
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Keyword(s):
We give explicit constructions of semigroups and operators with particular properties. First we build a bounded C0-semigroup which is invertible and which is not similar to a semigroup of contractions. Afterwards we exhibit operators which admit bounded imaginary powers of angle ω > 0 on a Hilbert space but which do not admit a bounded functional calculus on the sector of angle ω. (This gives the limit of McIntosh's fundamental result.) Finally we build, in the 2-dimensional Hilbert space, an operator which is not the negative generator of a semigroup of contractions, although its imaginary powers are bounded by eπ|s|/2.
1996 ◽
Vol 60
(1)
◽
pp. 51-89
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Keyword(s):
2017 ◽
Vol 5
(2)
◽
pp. 177-188
Keyword(s):
2009 ◽
Vol 80
(1)
◽
pp. 83-90
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2005 ◽
Vol 79
(3)
◽
pp. 391-398
Keyword(s):
1989 ◽
Vol 32
(3)
◽
pp. 320-326
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2015 ◽
Vol 14
(1)
◽
pp. 121-128
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