A note on the spectral operators of scalar type and semigroups of bounded linear operators.
Markin, Marat V. (2002)
International Journal of Mathematics and Mathematical Sciences
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Markin, Marat V. (2002)
International Journal of Mathematics and Mathematical Sciences
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(1997)
Banach Center Publications
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Markin, Marat V. (2004)
International Journal of Mathematics and Mathematical Sciences
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Roman Drnovšek (1997)
Studia Mathematica
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We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.
Jaromír J. Koliha, Trung Dinh Tran (2003)
Czechoslovak Mathematical Journal
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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions...
Timothy Randolph, Paul Patterson (1994)
Studia Mathematica
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Gogodze, Ioseb K., Gelashvili, Koba N. (1997)
Memoirs on Differential Equations and Mathematical Physics
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L. A. Coburn, R. G. Douglas (1971)
Publications Mathématiques de l'IHÉS
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Wolfgang Arendt, Alessandro Zamboni (2010)
Studia Mathematica
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Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection....
Piotr Budzyński, Jan Stochel (2007)
Studia Mathematica
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Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group...
Mastinšek, M. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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Piotr Budzyński, Jan Stochel (2009)
Studia Mathematica
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In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition...