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Toeplitz Operators on the Segal — Bargmann Space of Infinitely Many Variables

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Linear Operators in Function Spaces

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 43))

Abstract

The importance of Toeplitz operators acting on the Segal — Bargmann space B N (also referred to as the Fock space) became clear when V. Bargmann obtained in [1], [2] a model for certain quantum mechanics operators. Such fundamental concepts as the creation, or annihilation operators (of a Bose gas particle at state ej) can be represented as Toeplitz operators on BN, the symbols being the coordinate functions zj on C N, or their complex conjugates z̄j.

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References

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Authors and Affiliations

  1. Instytut Matematyczny PAN, ul. Solskiego 30, 31-027, Kraków, Poland

    J. Janas & K. Rudol

Authors
  1. J. Janas
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  2. K. Rudol
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Editor information

Editors and Affiliations

  1. Department of Mathematics, INCREST, Bd. Păcii 220, 79622, Bucharest, Romania

    H. Helson , B. Sz.-Nagy  & F.-H. Vasilescu ,  & 

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© 1990 Birkhäuser Verlag Basel

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Janas, J., Rudol, K. (1990). Toeplitz Operators on the Segal — Bargmann Space of Infinitely Many Variables. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_15

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  • DOI: https://doi.org/10.1007/978-3-0348-7250-8_15

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7252-2

  • Online ISBN: 978-3-0348-7250-8

  • eBook Packages: Springer Book Archive

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