A generalized winding number formula for the Witten index of a Toeplitz operator
Masaki Izumi
TL;DR
This paper extends the winding number formula from the Fredholm index to the Witten index for Toeplitz operators and introduces trace formulas involving operator monotone functions.
Contribution
It generalizes the winding number formula to the Witten index and develops trace formulas with Toeplitz operators and operator monotone functions.
Findings
Winding number formula is extended to the Witten index.
Trace formulas involving Toeplitz operators are established.
The approach links topological invariants with operator theory.
Abstract
We generalize the winding number formula for the Fredholm index of a Toeplitz operator to the Witten index. We also show trace formulae involving Toeplitz operators and operator monotone functions.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Holomorphic and Operator Theory · Matrix Theory and Algorithms