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Invariant Gaussian measures for operators on Banach spaces and linear dynamics
Author(s) -
Bayart Frédéric,
Grivaux Sophie
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl013
Subject(s) - mathematics , banach space , eigenvalues and eigenvectors , invariant measure , separable space , measure (data warehouse) , pure mathematics , invariant (physics) , degenerate energy levels , gaussian , mathematical analysis , mathematical physics , physics , quantum mechanics , database , computer science , ergodic theory
We give conditions for an operator T on a complex separable Banach space X with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non‐degenerate invariant Gaussian measure with respect to which it is weak‐mixing. The existence of such a measure depends on the geometry of the Banach space and on the possibility of parametrizing the ‐eigenvector fields of T in a regular way. We also investigate the connection with frequent hypercyclicity.