Opuscula Math. 25, no. 1 (2005), 139-148

Opuscula Mathematica

# A note on inductive limit model of Bargmann space of infinite order

Jerzy Stochel

Abstract. It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction $$a=(a_1,a_2,\ldots) \in l^2$$ are inductive limits of the creation and annihilation operator acting on Bargmann space of $$n$$-th order.

Keywords: Hilbert space, Bargmann space, creation operator, annihilation operator, inductive limit.

Mathematics Subject Classification: 47B38, 47B37, 47A80.

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• Jerzy Stochel
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland