A skew normal dilation on the numerical range of an operator

Putinar, Mihai; Sandberg, Sebastian

doi:10.1007/s00208-004-0585-3

Cited by 15 publications

(20 citation statements)

References 8 publications

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“…We refer the reader also to the series of papers [3,5,[11][12][13]43], where the relationships between the notions of dilation, boundedness of functional calculus and numerical range are studied for general convex domains.…”

Section: Proof Of Theorem 51 (I) ⇔ (I )mentioning

confidence: 99%

Resolvent characterisation of generators of cosine functions and C 0-groups

Król

2013

J. Evol. Equ.

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Abstract. The paper provides new characterisations of generators of cosine functions and C 0 -groups on UMD spaces and their applications to some classical problems in cosine function theory. In particular, we show that on UMD spaces, generators of cosine functions and C 0 -groups can be characterised by means of a complex inversion formula. This allows us to provide a strikingly elementary proof of Fattorini's result on square root reduction for cosine function generators on UMD spaces. Moreover, we give a cosine function analogue of McIntosh's characterisation of the boundedness of the H ∞ functional calculus for sectorial operators in terms of square function estimates. Another result says that the class of cosine function generators on a Hilbert space is exactly the class of operators which possess a dilation to a multiplication operator on a vector-valued L 2 space. Finally, we prove a cosine function analogue of the Gomilko-Feng-Shi characterisation of C 0 -semigroup generators and apply it to answer in the affirmative a question by Fattorini on the growth bounds of perturbed cosine functions on Hilbert spaces.

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Section: Proof Of Theorem 51 (I) ⇔ (I )mentioning

confidence: 99%

Resolvent characterisation of generators of cosine functions and C 0-groups

Król

2013

J. Evol. Equ.

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“…The universal constant C W (T ) has a geometric character, revealed a long time ago by studies studies in potential theory [22]. We will call it the (Carl) Neumann constant of the convex set.…”

Section: 1mentioning

confidence: 99%

“…We will call it the (Carl) Neumann constant of the convex set. For examples the reader can consult [6,22]. The idea behind the proof of (6) is the following.…”

Section: 1mentioning

confidence: 99%

“…This would requires functoriality transforms for the numerical range of a linear operator, and there are very few positive results in this direction, see [22] and the references cited there. Second, what happens if a compact set is defined by a non-archimedian cone?…”

Section: One Complex Variable Note That the Definition Of The Archimmentioning

confidence: 99%

“…This is due to the fact that the semi-spectral measure measure E T appearing in the Fanttapiè or double layer potential transforms is non-negative. We refer to [16,22] for details.…”

Section: Subnormal Tuplesmentioning

confidence: 99%

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