The tame symbol and determinants of Toeplitz operators
Efton Park

TL;DR
This paper derives an explicit formula for the determinant of a product of Toeplitz operators and their inverses using tame symbols, linking operator theory with complex analysis.
Contribution
It introduces a novel explicit formula connecting Toeplitz operator determinants with tame symbols of their symbols on the unit disk.
Findings
Explicit determinant formula involving tame symbols
Connection between Toeplitz operators and algebraic symbols
Extension of classical results to meromorphic symbols
Abstract
Suppose that and are smooth complex-valued functions on the circle that are invertible, have winding number zero with respect to the origin, and have meromorphic extensions to an open neighborhood of the closed unit disk. Let and denote the Toeplitz operators with symbols and respectively. We give an explicit formula for the determinant of in terms of the products of the tame symbols of and on the open unit disk.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Algebraic and Geometric Analysis
