Analysis Seminar

October 5, 2011

Swarup Ghosh, Bowling Green State University

Title: Peak Points and Gleason Parts in R(X) (Part I)

Abstract:  Peak points and Gleason parts are two important notions in the function theory. In this talk, we will first define peak points and Gleason parts. Then we will discuss some relations between these two notions. Here R(X) denotes the uniform closure of the collection of all rational functions with no poles on C, a compact subset of the complex plane.

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October 12, 2011

Swarup Ghosh, Bowling Green State University

Title: Peak Points and Gleason Parts in R(X) (Part II)

Abstract: Peak points and Gleason parts are two important notions in the function theory. Since we have seen the definition and properties of peak points already, in this talk, we will first define Gleason parts. Then we will discuss some relations between these two notions. Here R(X) denotes the uniform closure of the collection of all rational functions with no poles on X, a compact subset of the complex plane.

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October 19, 2011

Swarup Ghosh, Bowling Green State University

Title: Peak Points and Gleason Parts in R(X) (Part III)

Abstract: Peak points and Gleason parts are two important notions in the function theory. In this talk, we will prove that in R(X), if a point is not a peak point, then the Gleason part corresponding to that point has positive Lebesgue measure. Then we will derive some important facts about these two notions in R(X). Here R(X) denotes the uniform closure of the collection of all rational functions with no poles on X, a compact subset of the complex plane.

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October 26, 2011

Leonardo Pinheiro, Bowling Green State University

Title: Every Chaotic Operator Satisfies the Hypercyclicity Criterion

Abstract: It is a well-known fact that not every hypercyclic operator on a Banach Space satisfies the Hypercyclicity Criterion. In this talk we show that every hypercyclic operator with a dense set of points whose orbits are 'nice' will satisfy the Hypercyclicity Criterion. In particular, every chaotic operator satisfies the Criterion.

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November 2, 2011

Gokul Kadel, Bowling Green State University

Title: Topological Dynamics - Part I

Abstract:We will discuss some results from a chapter of the book "Linear Chaos", by K. Grosse-Erdmann and A. Peris.  

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November 9, 2011

Gokul Kadel, Bowling Green State University

Title: Topological Dynamics - Part II

Abstract: We will discuss some results from a chapter of the book "Linear Chaos", by K. Grosse-Erdmann and A. Peris.

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November 16, 2011

Alex Izzo, Bowling Green State University

Title: Function algebras invariant under group actions

Abstract: Motivated by his work on a conjecture of William Arveson in operator theory, Ronald Douglas raised the following question, where S denotes the unit sphere in complex n-space. If A is a function algebra on S that contains the ball algebra A(S) and whose maximal ideal space is S, and if A is invariant under the action of the n-torus on S, does it follow that A = C(S)? We will discuss the solution to Douglas' question and present related results that were motivated by the question.

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November 30, 2011

Yun-Su Kim

Title: Hilbert Spaces with respect to Operator-Valued Norm

Abstract: We introduce two kinds of operator-valued norms. One of them is an L(H)-valued norm. The other one is an L(C(K))-valued norm. We provide the notion of a Hilbert space with respect to an L(H)-valued norm. By a Hilbert space with respect to an L(H)-valued norm, we generalize the notion of a Hilbert space. Furthermore, we provide several interesting examples (L-infinity and C(Y)) of Hilbert spaces with respect to an operator-valued norm.

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