Participant Testimonials
The conference enabled me to continue some collaborations in progress and made me aware of some new work that is closely related to things I had done years ago on the C(alpha) spaces and may lead to additional results. In addition I was able to talk to a prospective postdoc, Dosev, and we subsequently completed arrangements for him to spend next year in Stillwater.
Mathematics, Oklahoma State University
The workshop kept me up to date with a field of research close to mine. I had new contacts that I wouldn't have had otherwise. Feedback about my talk helped me improve a paper.
Mathematics, Texas A&M University
During the workshop, I had an idea for a proof that originated a paper that is almost ready now (tentatively entitled "A new proof of Pietsch's composition theorem"). Also, a question after my talk made me realize a result that followed from what I already had. Moreover, another comment made me aware of the fact that I was looking at a situation well understood in categorical Banach space theory; I am now in the process of incorporating these categorical methods into my research. Thanks to the workshop, I got invited to give a talk at another conference. I don't think this would have happened if I had not been there.
Department of Mathematics, Texas A&M University
The workshop gave an impulse to my current research, essentially by talking with people I already collaborated with, as well as opening possibilities of organizing future events with some people I met at the workshop.
I would like to thank you and the organizers of BIRS 12w5019 for doing an outstanding job on organizing this workshop. It is perhaps the best conference, evaluating facilities, attendance and scientific program, I've ever attended. Best regards,
I learned that a problem I was very much interested in on commutators had been solved by Matt Tarbard. Since he did not know that his example solved the problem, it was good that I was in the audience when he spoke. I was struck by the depth in the development of the infinite dimensional theory. Due to the work of the Argyros and Odell-Schlumprecht schools, we have a completely different picture of the structure of general Banach spaces than we had a few years ago. It was gratifying to see how many good young people are working in the field.
1. I worked on current projects with current coauthors. 2. I discussed possible future projects with recent coauthors. 3. Most importantly, I met new people with whom I discussed possible future projects. 4. The whole atmosphere was very inspiring.
I found the workshop very inspiring and thoroughly enjoyable. There was a good mix between people specializing in various directions of Banach space theory. I definitely made some new connections and learnt some new results relevant for my ongoing research.
The workshop was excellent in every way. The talks were of very high quality. I was introduced to the latest directions in research in Banach space theory. I also had the chance of interacting with colleagues to discuss possible joint projects.
In general, my participation in the BIRS workshop has only had a positive impact upon me, in every aspect. Indeed, i was given the chance to get more familiar with fields i was not involved in so far, as well as offered the opportunity to become better informed about methods and results concerning my main field of study. Since i am a young researcher, the workshop was an excellent way for me to meet other researchers, young and more experienced alike, which led to various scientific discussions, offering the prospect of new collaborations and papers. Since i still have a few years ahead of me in order to obtain my Ph.d, my job prospects may not be a matter of primary concern to me, nevertheless i believe that coming in touch with all these members of the scientific community will have a positive influence on this aspect in the future.
The workshop was very fruitful for my current and future research, thanks to new methods I got more familiar with during the workshop and new research projects which I started there - also in collaboration with other participants. I appreciate very much the talks delivered during the workshop as well as the possibility of discussion with other researchers I don't have opportunity to meet often.
The participation in the workshop was very stimulating for me. I learned about new advances in the field. In particular, after the talk of Christian Rosendal, I realized that his new joint paper with Ferenczi is related to my old work on isometries. I started a new cooperation with Steve Dilworth and we expect to answer some of the problems described by Ferenczi and Rosendal in their paper (some of these questions are quite old, but the new approach of Ferenczi and Rosendal shed very good light on them). Without coming to the workshop it is highly unlikely that I would have known about this modern approach and that I would contribute to the solutions of these problems. I expect that Steve Dilworth and I will have a paper about this coming out in the fall. I also had a chance to discuss another research project with Gideon Schechtman and Bill Johnson. This project was not directly related to the theme of the workshop, but it was a great opportunity to meet and be able to discuss the problem in person. This will also lead to a joint publication with Gideon Schechtman. Seeing many young people at the conference was very valuable to me as a member of the hiring committee at my department. We may be able to offer some temporary positions to some people I met at the workshop, this is still uncertain in the present economic situation, but I am working towards it.
This was a splendid conference,one of the best I've ever been to, and I've been to a lot! All of the talks were at an exceptionally high level,and well illustrated the great diversity in our field of research-hats off to the organizers! Informal discussions ,some with people I'd never met, produced very stimulating questions and new directions of research. In particular, i'd like to mention the following questions which emerged during the workshop. Let X be a separable Banach space with the bounded approximation property. Is the double dual of the space of compact operators on X non-separable? An affirmative answer would show there cannot be a reflexive Banach space with the approximation property such that every operator on it is compact + scalar multiple of the identity. But here is an approach,which in any case points to a new fundamental object associated with this problem. Suppose X has a monotone basis,and let Se denote the space of sequences tending to zero,which act as bounded operators on the basis by multiplication,endowed with the operator norm. A beautiful argument shown me by Ted Odell shows that every sequence tending to 0, of bounded variation belongs to Se. Is Se^** non-separable? Even if one could simply show that Se is not quasi-reflexive, the above mentioned problem about reflexive spaces would have a negative answer. The conference greatly helped me crystallize my thinking concerning the Invariant Subspace problem, Although I believe i am close to a negative solution to the Hyper-Invariant subspace problem (for Hilbert space), I understood during the conference that results I've already obtained yield a new direction in research in classical harmonic analysis,of independent interest. Furthermore, i discovered formulations of a "suitable" class of Banach spaces for which my ideas would work,if they carry through for Hilbert space itself. Finally, I started a joint project with a young guy from Canada,concerning the following open problem If an operator on a complex Banach space has the unit circle as it's spectrum,but no point spectrum,does it have a log? i conjecture that my recently discovered weighted invertible bilateral shift is a counterexample. Of course the organizers created a marvelous,warm atmosphere during the entire conference. a most enjoyable and highly stimulating experience!
Department of Mathematics, University of Texas at Austin
My participation helped established a new cooperation on a paper to be written. This collaboration would most probably have taken place also without the conference but it would have been much more time consuming and painful. I think the participation of my postdoc, Detelin Dosev, (and of Dale Alspach, Bill Johnson and myself) helped him secured a job at Oklahoma State University next year.
The Banach space conference was excellent and I had the opportunity to learn about new developments and talk with mathematicians I haven't met before. I also worked with a colleague present at the conference on a project of common interest and we arranged to meet again over the summer to continue our collaboration. The setting of the conference, the organization, accommodations, facilities, are all very very good.
I enjoyed the Banach space workshop enormously. The program was mathematically exceptionally strong with a number of very deep and difficult results on constructions of some special spaces with very few bounded operators and on related structures in arbitrary Banach spaces or in algebras B(X). Several "more fundamental" general lectures presented perspectives (and some technicalities) of the theory of infinite-dimensional Banach spaces in the last several years and pointed out directions for the future. These lectures were complemented by shorter technical talks illustrating concrete recent results and methods, given by a number of obviously very talented researchers of younger generation. Most of talks were on a highest scientific level, and all were interesting. I could not pick talks to miss would I want to "play hooky" so as a result I attended all of them (!). To tell the truth this was quite an unusual experience for me. I discussed that with some other "senior" friends and we were all very impressed especially by a quality and a number of young people in the area. I was happy to see breakthrough developments of recent years, especially the construction of Argyros and Haydon which has as a starting point Bourgain--Delbaen's space from the late 1970's. In Banff i started to understand some other potential ideas closer to my own research. It was a very stimulating meeting.
The workshop: Banach space theory did have positive impact on my current research. There were several new results about closed ideals and commutators of operators on certain Banach spaces. These are the topics I am currently working on. I also got to know some people working on Banach space theory from Europe whom I never met before.
