Non-commutative chaotic expansion of Hilbert-Schmidt operators on Fock space

DOI10.1007/BF02101623zbMath0843.46046MaRDI QIDQ1912608

Stéphane Attal

Publication date: 13 May 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

chaotic expansion of random variablesHilbert-Schmidt operator on the Fock spaceMaassen-Meyer kernelnon-commutative stochastic integrals

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Quantum stochastic calculus (81S25) Stochastic integrals (60H05)

Related Items (2)

A \(W\)-transform-based criterion for the existence of bounded extensions of \(E\)-operators. ⋮ Analytic characterization for Hilbert-Schmidt operators on Fock space

Cites Work

• Quantum Ito's formula and stochastic evolutions
• Stochastic integral representation of bounded quantum martingales in Fock space
• Quantum probability for probabilists
• An algebra of non-commutative bounded semimartingales: Square and angle quantum brackets
• Multiple Wiener integral
• Tensor Algebras Over Hilbert Spaces. I
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