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010 a| 2021016944;

020 a| 9781470446635q| (paperback);

020 z| 9781470464684q| (pdf);

035 a| (WaSeSS)ssj0002470745;

049 a| EREEa| NEHH;

050 00 a| QA322.4b| .G75 2021;

082 00 a| 515/.7332| 23;

084 a| 47A16a| 37A05a| 54E52a| 54H052| msc;

100 1 a| Grivaux, S.?| UNAUTHORIZED;

245 10 a| Linear dynamical systems on Hilbert spacesh| [electronic resource] :b| typical properties and explicit examples /c| S. Grivaux, É. Matheron, Q. Menet.;

260 a| Providence :b| American Mathematical Society,c| [2021];

263 a| 2107;

300 a| pages cm.;

490 0 a| Memoirs of the American Mathematical Society ;v| Number 1315;

504 a| Includes bibliographical references.;

506 a| Available only to authorized users.;

520 a| "We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigenvalues and admits no non-trivial invariant measure, but is densely distributionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form "diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift" is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Hilbert space.=| ^A50564;

650 0 a| Linear systems.=| ^A201193;

650 7 a| Operator theory -- General theory of linear operators -- Cyclic vectors, hypercyclic and chaotic operators.2| msc;

650 7 a| Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Ergodic theory [See also 28Dxx] -- Measure-preserving transformations.2| msc;

650 7 a| General topology {For the topology of manifolds of all dimensions, see 57Nxx} -- Spaces with richer structures -- Baire category, Baire spaces.2| msc;

650 7 a| General topology {For the topology of manifolds of all dimensions, see 57Nxx} -- Connections with other structures, applications -- Descriptive set theory (topological aspects of Borel, analytic, proj2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Matheron, Étienne.?| UNAUTHORIZED;

700 1 a| Menet, Q.,d| 1988-?| UNAUTHORIZED;

856 40 z| Full text available from Memoirs of the American Mathematical Societyu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.ams.org%2Fmemo%2F1315%2F;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5820410-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 5/13/2022x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5820410-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 5/13/2022x| EBOOKz| JERESOURCE;

Linear dynamical systems on Hilbert spaces typical properties and explicit examples / S. Grivaux, É. Matheron, Q. Menet.

Author/creator	Grivaux, S.
Other author	Matheron, Étienne.
Other author	Menet, Q., 1988-
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	pages cm.
Supplemental Content	Full text available from Memoirs of the American Mathematical Society
Subjects	Hilbert space. Linear systems.

Series	Memoirs of the American Mathematical Society ; Number 1315
Abstract	"We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigenvalues and admits no non-trivial invariant measure, but is densely distributionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form "diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift" is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2021016944
ISBN	9781470446635 (paperback)
ISBN	(pdf)

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Linear dynamical systems on Hilbert spaces typical properties and explicit examples / S. Grivaux, É. Matheron, Q. Menet.

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