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Vladimir Gurariy Conference

The Department of Mathematical Sciences of Kent State University is planning a Conference to Celebrate the Life and Work of Vladimir Gurariy.

The meeting will take place on Friday-Saturday, March 10-11, 2006. There will be several components to this meeting which will only be able to touch on the contributions, in so many different areas, that Vladimir made.

In particular, speakers at the meeting will include Per Enflo (Kent), Wolfgang Lusky (Paderborn), Mikhail Ostrovskii (New York), Peter Sarnak (Princeton), and Juan Seoane (Kent).

We anticipate several other speakers, and we also invite participants to offer talks at this meeting. In addition, there will be a concert on Friday evening featuring performances of piano and vocal music composed by Vladimir. It will be a great help to the organizers if people could let us know of their intended participation.

For More information, please, contact Richard Aron (aron@math.kent.edu), Joe Diestel (j_diestel@hotmail.com), Per Enflo (enflo@math.kent.edu), Victor Lomonosov (lomonoso@math.kent.edu), Andrew Tonge (tonge@math.kent.edu), or Artem Zvavitch ( zvavitch@math.kent.edu).

Schedule

Friday, March 10, 2006 (Lecture Theater, Liquid Crystals Institute)

3:05 PM  Welcome and Introduction, by Andrew Tonge

3:15 PM  Mikhail Ostrovskii (St. John’s University, New York),

“Problems related to the notion of opening between subspaces of a Banach space”

4:15 PM  Refreshments

4:45 PM  Juan Seoane  (Kent State University)

“Lineability, Spaceability, and Vladimir

Abstract: We will give a report on the paper “Lineability and spaceability of sets of functions on R”, recently published in the journal Proceedings of the AMS. This paper was a joint collaboration with Vladimir and Richard M. Aron. At that time, Vladimir was very interested (amongst other things) in the study of large algebraic structures (infinite dimensional vector spaces, Banach spaces, or algebras) enjoying certain large or exotic properties, such as being a continuous nowhere differentiable function, a differentiable nowhere monotone function, or being everywhere surjective.

Vladimir coined the concepts of lineable, spaceable, and algebrable to refer to the existence of large vector spaces, closed spaces, and algebras, respectively, of functions on R or C[0,1] enjoying some of these so called exotic properties.

We will give an overview on the main results from this joint paper with Vladimir and Richard M. Aron, as well as an historical view of the progress of Vladimir in these concepts that he created.

5:45 PM  Larisa Altshuler (Kent State University)

Photographic presentation of Vladimir, colleagues, and friends

6:30 PM  Reception  (MSB Library)

8:00 PM  Concert, Music & Speech Building, Choir Room (E 112)

Featuring Per Enflo, Piano, and Eugene Gurariy, Voice

Saturday, March 11, 2006:  Room 228 MSB

9:45 AM - 12:30 PM   Invited Student Talks

9:50 – 10:10 AM Dan Radelet (University of Pittsburgh) 

“The Mazur Product map” Abstract:  Given two convergent sequences x and y, and given z their Cauchy product, we ask whether every convergent sequence is of the form .  We are able to use Cesaro averaging and factorizations on Hardy space to demonstrate that this product mapping with domain c × c is not onto.  Further, we are able to show that the mapping is not onto for larger domain spaces containing c0 and l.

10:15 – 10:35 AM  Francisco García (Kent State University)

“Rotundity, smoothness and renormings in Banach spaces”

Abstract: Characterizations of rotundity and smoothness in terms of faces and exposed faces of the unit ball are shown and some others are discussed.

10:40 – 11:00 AM Abebaw Tadesse (University of Pittsburgh)

“Compact composition operators on the Hardy and Bergman spaces’’

Abstract: In this talk, we investigate compact composition operators which are not Hilbert-Schmidt. We consider the class of examples (B. A. Lotto (1992)) of composition operators whose symbol  is a Riemann map from the unit disk D onto the semi-disk with center (½ ,0)  radius ½, and, in general, onto a crescent-shaped regions constructed based on this semi-disk. 

We use the R. Riedel (1994) characterization of -boundedness/compactness on H to determine the range of values of in R for which  is -bounded/compact. In particular, we show that the class of Riemann maps under consideration gives example(s) of -bounded composition operators which fail to be -compact (0 < < ∞.) This was an open question raised by Hunziker and Jarchow (1991)(Section 5.2). Finally, we prove a necessary condition for to be Hilbert--Schmidt in terms of -boundedness. This result arises from our attempt to generalize previous observations to relate Hilbert-Schmidt classes with -bounded/compact operators.

11:00 – 11:10 AM  COFFEE,   MSB 3rd FLOOR LOUNGE  

11:20 – 11:40 AM  Jerry Day (University of Pittsburgh) 

“All minimal invariant sets of Alspach’s map’’

Abstract: In 1981, Dale Alspach introduced the baker transform as an example of a non-expansive map on a weakly compact convex set that is fixed point free.  The minimal invariant sets for this mapping have been of particular interest.  Recent work of C. Lennard and the presenter has shed some light on this topic.  Specifically, a method for finding all minimal invariant sets of Alspach's map will be presented, and a constructive definition of these sets will be given.

11:45 – 12:05 PM Aderaw Fenta (Kent State University)

“Bases and Lacunary Power Sequences in C and Lp

Abstract: Some of V. I. Gurariy’s works (1963 - 1971) in the areas of bases and basic sequences in uniformly convex and uniformly smooth spaces will be revisited. His paper with Macaev on lacunary power series  in C and Lp will be discussed and some extensions of their results will be considered.

12:10 – 12:30 PM Alfy Dahma (University of Pittsburgh) 

“Functions with a positive Fourier transform”

Abstract: One of the main goals in Fourier Analysis is to recover an L1 function from its Fourier transform. In this talk I will review some basic results concerning the Fourier transform and discuss a condition under which the Inversion Theorem may be applied.

12:30 – 1:30 PM   Lunch  (MSB 3rd Floor Lounge)

1:30 PM    Room 228 MSB

Maria D. Acosta (University of Granada)

“Some Banach spaces where all the slices of the unit ball are large”

Per Enflo (Kent State University)

“Vladimir and me”

Chris Lennard (University of Pittsburgh)

“A characterization of frames in terms of Riesz bases”

Abstract: We present a characterization of frames for a Hilbert space in terms  of the average of two Riesz bases for a Hilbert superspace.

Wolfgang Lusky (University of Paderborn)

“Geometry of Müntz Spaces”

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