Fredholmness of Toeplitz operators on the Fock space

Abstract

The Fredholm property of Toeplitz operators on the $p$-Fock spaces $F_{\alpha }^p$ on ${\mathbb{C}}^n$ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra ${\mathcal{T}}_{p,\alpha }$ on $F_{\alpha }^p$ in terms of the invertibility of limit operators is derived. This paper is based on previous work, which establishes corresponding results on the unit balls ${\mathbb{B}}^n$.

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References in corpus (2)

• An Affirmative Answer to a Core Issue on Limit Operators
• Duality in Segal-Bargmann Spaces

Cited by in corpus (5)

• Correspondence theory on $p$-Fock spaces with applications to Toeplitz algebras
• Limit operators techniques on general metric measure spaces of bounded geometry
• Fredholm Toeplitz operators on doubling Fock spaces
• Heisenberg-smooth operators from the phase space perspective
• Toeplitz algebra on the Fock space