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[PAST EVENT] On the algebras generated by Toeplitz operators with piecewise continuous symbols
April 12, 2013
2pm - 3pm
We explain an apparent disagreement between the fact that the Fredholm symbol algebras of two different C*-algebras generated by Toeplitz operators with piecewise continuous symbols, acting on the Hardy space and acting on the Bergman space, have the same Fredholm symbol algebras and the same symbol homomorphism on generating operator, and the fact that the initial generators of these algebras are not unitary equivalent modulo compact operators.
As it turns out, although the initial generators are not unitary equivalent modulo compact operators, the two above C*-algebras are unitary equivalent. The initial generators of either one of these algebras are unitary equivalent to certain elements of another algebra. In both cases the symbol homomorphism is generated by the same mapping of the corresponding generators, but, when compared, it differs on the parameterization of the auxiliary segments [0,1]. The explicit connection between the parameterizations is given.
As it turns out, although the initial generators are not unitary equivalent modulo compact operators, the two above C*-algebras are unitary equivalent. The initial generators of either one of these algebras are unitary equivalent to certain elements of another algebra. In both cases the symbol homomorphism is generated by the same mapping of the corresponding generators, but, when compared, it differs on the parameterization of the auxiliary segments [0,1]. The explicit connection between the parameterizations is given.