On the product formula for Toeplitz and related operators
Jani A. Virtanen
TL;DR
This paper revisits known product formulas for Toeplitz operators, exploring their applications in Fredholmness, boundedness, and Berezin-Toeplitz quantization, while highlighting open problems in the field.
Contribution
It provides a comprehensive review of product formulas for Toeplitz operators and discusses their implications in various analytical contexts.
Findings
Revisited classical product formulas for Toeplitz operators.
Explored applications to Fredholmness and boundedness.
Identified open problems in Toeplitz operator theory.
Abstract
In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems are also mentioned.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Advanced Algebra and Geometry