Measure of the Banach limit on \(L_\infty(\mathbb{R})\)

DOI10.1134/S1995080224603138MaRDI QIDQ6648984

Vladimir Andreevich Glazatov

Publication date: 5 December 2024

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

invariant measurefinitely additive measureBanach limitKoopman representationA. Weil's theorem

Mathematics Subject Classification ID

Set functions and measures on spaces with additional structure (28Cxx) General mathematical topics and methods in quantum theory (81Qxx) General quantum mechanics and problems of quantization (81Sxx)

Cites Work

• Title not available (Why is that?)
• Averaging of random walks and shift-invariant measures on a Hilbert space
• Hamiltonian approach to secondary quantization
• Analogs of the Lebesgue measure in spaces of sequences and classes of functions integrable with respect to these measures
• Schrödinger quantization of infinite-dimensional Hamiltonian systems with a nonquadratic Hamiltonian function
• Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators
• The main classes of invariant Banach limits
• Factorization of Summability-Preserving Generalized Limits
• Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups
• Direct limit of shift-invariant measures on a Hilbert space
• Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows

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