Operator Theory Seminar

The Operator Theory Seminar meets

which is the seminar room for the IUPUI Department of Mathematical Sciences.

    The operator theory seminar is a working seminar for students and others who want to learn about this kind of mathematics as well as a forum for participants to present new work, of their own or the work of others, or to read together related function theory or functional analysis. All are welcome!

Questions about the seminar and requests to be added to the mailing list can be directed to Carl Cowen: ccowen "at" iupui "dot" edu

The Seminar in Previous Semesters

FALL 2008

December 3 (Last meeting of the semester)

William Higdon (University of Indianapolis)

On The Numerical Range Of A Class Of Composition Operators on H^2

November 26

No Meeting -- Thanksgiving Break

November 19

Discussion on problems in Operator Theory

November 12

Morteza Seddighin (IU East)

Anti-eigenvalues and Operator Inequalities

Abstract

The Kantrovich inequality and Kantrovich-like inequalities for positive bounded operators have had many applications in operator theory, and other areas since 1948. The concept of Antieigenvalue or the operator cosine was independently introduced in 1967 by Karl Gustafson for use in perturbation of semigroup generators. For a positive operator, both the Kantorovich inequality and the value of operator cosine are expressed in terms to the smallest and largest eigenvalues of the operator, and it turns out that the former is obtained from the latter. We will discuss the extensions of Kantorovich inequality and Antieigenvalue to other classes of operators.

November 5

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class (continued)

October 29

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class (continued)

October 22

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class (continued)

October 15

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class (continued)

October 8

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class (continued)

October 1

Carl Cowen (IUPUI)

Maps of the unit ball in the Schur-Agler Class

September 24

Carl Cowen (IUPUI)

A class of analytic maps of the unit ball in C^N into itself

September 17

Carl Cowen (IUPUI)

Hermitian Weighted Composition Operators on Weighted Hardy Spaces (continued)

September 10

Carl Cowen (IUPUI)

Hermitian Weighted Composition Operators on Weighted Hardy Spaces (continued)

September 3

Carl Cowen (IUPUI)

Hermitian Weighted Composition Operators on Weighted Hardy Spaces

This talk describes work of Gajath Gunatillake, Eungil Ko, and the speaker that extends work in an earlier paper that describes the operators of the title acting on the usual Hardy Hilbert space. A 'Weighted Hardy Space' is a Hilbert space of functions analytic on the unit disk in which the polynomials are dense and the monomials are an orthogonal set. The usual Hardy space, the Dirichlet space, the Bergman space, and weighted Bergman spaces with a radially symmetric wieght function are all examples of a weighted Hardy space.

Necessary conditions for weighted composition operator are given for arbitrary weighted Hardy spaces and these are used to identify all the Hermitian weighted composition operators on the standard Bergman space. In addition, the results on weighted composition operators are used to find the extremal functions, related to contractive divisors, for some specific invariant subspaces for multiplication by z on the Bergman space. for

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