Algebraic Methods in Functional Analysis: The Victor Shulman Anniversary Volume

301 Pages·2014·2.94 MB·English

by  Ivan G. Todorov

Operator Theory
Advances and Applications
233
Ivan G. Todorov
Lyudmila Turowska
Editors
Algebraic
Methods in
Functional
Analysis
The Victor Shulman Anniversary
Volume

Operator Theory: Advances and Applications
Volume 233

Founded in 1979 by Israel Gohberg

Editors:
Joseph A. Ball (Blacksburg, VA, USA)
Harry Dym (Rehovot, Israel)
Marinus A. Kaashoek (Amsterdam, The Netherlands)
Heinz Langer (Vienna, Austria)
Christiane Tretter (Bern, Switzerland)

Associate Editors: Honorary and Advisory Editorial Board:
Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA)
Wolfgang Arendt (Ulm, Germany) Ciprian Foias (College Station, TX, USA)
Albrecht Böttcher (Chemnitz, Germany) J.William Helton (San Diego, CA, USA)
B. Malcolm Brown (Cardiff, UK) Thomas Kailath (Stanford, CA, USA)
Raul Curto (Iowa, IA, USA) Peter Lancaster (Calgary, Canada)
Fritz Gesztesy (Columbia, MO, USA) Peter D. Lax (New York, NY, USA)
Pavel Kurasov (Stockholm, Sweden) Donald Sarason (Berkeley, CA, USA)
Leonid E. Lerer (Haifa, Israel) Bernd Silbermann (Chemnitz, Germany)
Vern Paulsen (Houston, TX, USA) Harold Widom (Santa Cruz, CA, USA)
Mihai Putinar (Santa Barbara, CA, USA)
Leiba Rodman (Williamsburg, VA, USA)
Ilya M. Spitkovsky (Williamsburg, VA, USA)

Subseries
Linear Operators and Linear Systems
Subseries editors:
Daniel Alpay (Beer Sheva, Israel)
Birgit Jacob (Wuppertal, Germany)
André C.M. Ran (Amsterdam, The Netherlands)

Subseries
Advances in Partial Differential Equations
Subseries editors:
Bert-Wolfgang Schulze (Potsdam, Germany)
Michael Demuth (Clausthal, Germany)
Jerome A. Goldstein (Memphis, TN, USA)
Nobuyuki Tose (Yokohama, Japan)
Ingo Witt (Göttingen, Germany)
Ivan G. Todorov
Lyudmila Turowska
Editors
Algebraic Methods in
Functional Analysis
The Victor Shulman Anniversary Volume
Editors
Ivan G. Todorov Lyudmila Turowska
Pure Mathematics Research Centre Mathematical Sciences
Queen’s University Belfast Chalmers University of Technology and
Belfast, UK the University of Gothenburg
Göteborg, Sweden

ISSN 0255-0156 ISSN 2296-4878 (electronic)
ISBN 978-3-0348-0501-8 ISBN 978-3-0348-0502-5 (eBook)
DOI 10.1007/978-3-0348-0502-5
Springer Basel Heidelberg New York Dordrecht London
Mathematics Subject Classification (2010): 47A, 47B, 47D, 47L, 47N. 46A, 46B, 46C, 46H, 46L

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Contents
Introduction ............................................................. vii
E. Kissin, V. Lomonosov and Yu. Turovskii
Victor Shulman: The Gentle Art of Mathematics .................... 1
J. Alaminos, J. Extremera and A.R. Villena
Operators Splitting the Arveson Spectrum .......................... 17
Y. Choi
Singly Generated Operator Algebras Satisfying
Weakened Versions of Amenability .................................. 33
E.T.A. Kakariadis and E.G. Katsoulis
Operator Algebras and C*-correspondences:A Survey ............... 45
A. Katavolos
Some Operator Algebras from Semigroups .......................... 75
T. Loring and T. Shulman
Lifting Algebraic Contractions in C*-algebras ....................... 85
M. Mathieu
The Second Local Multiplier Algebra of a Separable 𝐶*-algebra ..... 93
M.I. Ostrovskii
Test-space Characterizations of Some Classes of Banach Spaces ..... 103
S. Papapanayides and I.G. Todorov
Splittings of Masa-bimodules ........................................ 127
A.Yu. Pirkovskii
Noncommutative Analogues of Stein Spaces of
Finite Embedding Dimension ....................................... 135
P. Salmi
Idempotent States on Locally Compact Groups
and Quantum Groups ............................................... 155
vi Contents
V.S. Shulman and Y.V. Turovskii
Topological Radicals, V.
From Algebra to Spectral Theory ................................... 171
G. Weiss
A Brief Survey on
1. Infinite-dimensional Schur–HornTheorems and Infinite Majorization
Theory with Applications to Operator Ideals
2. 𝐵(𝐻)-subideals of Operators ..................................... 281
OperatorTheory:
Advances andApplications,Vol.233,vii–viii
⃝c 2014SpringerBasel
Introduction
Today,thesubjectofFunctionalAnalysisismoreactivethanever.Celebratingthe
contributionsofoneoftheleadingscientistsinthisfield,ProfessorVictorShulman,
has givenus the opportunity to presentin this volume a number of aspects of the
area that are closely related to his work. His contributions to Functional Analysis
are explained in greater detail in the article by E. Kissin, M. Lomonosov and Yu.
Turovskii, included in the present volume.
Algebraic methods havebeen used with greatsuccess in Functional Analysis
sinceitsverybeginnings.Inthe1930s,F.MurrayandJ.vonNeumannintroduced
what is known today as von Neumann algebras with the aim of formulating a
suitablemathematicallanguageforQuantumPhysics.Adecadelater,I.M.Gelfand
and M. Naimark developed the theory of C*-algebras. These two complementary
andsymbioticcontextshaveprovidedthegroundformanyofthealgebraicaspects
of Operator Theory in later years. They have been the starting point for the
development of hugely successful theories, such as Operator Space Theory in the
1980s and the Theory of Locally Compact Quantum Groups in the past decade.
Motivation for their development has come simultaneously from “single operator
theory”,thatis,fromthestudy ofthepropertiesofindividualoperatorsactingon
Hilbert space.
The more general setting of Banach spaces has been, both directly and in-
directly, essential for the development of many new ideas in Operator Theory;
indeed, it has been a motivating force in Operator Space Theory, serving at the
sametimeasthe“right”context,intermsofgenerality,forstudyingvariousoper-
atortheoreticquestions.LargepartsofHarmonicAnalysishaveenriched,andhave
benefited from,Functional Analysis;oneexample isthe study ofvariousclassesof
operators arising directly from the context of topological groups, such as Toeplitz
operators, while another one is Invariant Subspace Theory for non-selfadjoint op-
erator algebras, which has been influenced by Beurling’s theorem. The successful
functional analyticformulationofNon-commutativeHarmonicAnalysisbyP. Ey-
mard in the mid 1960s has had a decisive impact on the research in the field,
and has provided the base for the aforementioned developments in the theory of
locallycompactquantumgroups.Banach algebras, developedsimultaneouslywith
C*-algebras, have, on the other hand, provided a simple algebraic setting for the
study of a great number of analytical problems.
The present volume reflects, to a significant extent, all of the above settings
and presents the state-of-the-art of a number of subareas of Operator Theory. It
viii Introduction
is comprised of comprehensive survey articles and original research papers that
concern, among others, the following domains: the theory of C*-correspondences,
non-selfadjoint operator algebras and masa-bimodules, local multiplier algebras,
operatorideals,Banachspacegeometry,thetheoryoflinearpreserves,liftingprop-
erties in C*-algebras, the theory of topological algebras and the theory of locally
compactquantumgroups.Italsoincludesanarticleontopologicalradicals,which
is of a larger size than the rest of the contributions due to the vast scope of its
subject. The topics presented in the volume are currently undergoing intensive
development, and further progress on them is expected in the future.
The paperswererefereedby qualifiedexpertsinthe field.The Editorswould
liketothankallrefereesfortheirpromptadvice,whichhelpedimprovethevolume.
We wish to take the opportunity to thank all participants of the conference
and, in particular, the authors of the articles of these proceedings. Last, but not
least, we wouldlike to thank the SwedishResearchCouncil andthe Wenner-Gren
Foundation for providing the financial support, without which the meeting would
never have materialised.
8 December 2012 Ivan Todorov, Belfast
Lyudmila Turowska, Gothenburg
OperatorTheory:
Advances andApplications,Vol.233,1–16
⃝c 2014SpringerBasel
Victor Shulman:
The Gentle Art of Mathematics
E. Kissin, V. Lomonosov and Yu. Turovskii
It came as a bit of a shock to all of us:
Victor (or Vitya, as we affectionately call
himinRussian)is65.Holdon,thiscan’tbe
true!We justplayedfootballwithhimand
he scored a few goals. He was all over the
field – full of drive and the desire to win.
No, he cannot be 65! Don’t tell us about
his date of birth or the age of his children.
It just doesn’t make sense!
Itall startedwithanemailfromIvan
TodorovandLyudmilaTurowska.Theyin-
formed us that they were going to orga-
nizeamathematicalconferenceinGothen-
burg, Sweden in honour of the 65th an-
niversaryofProfessorVictorShulman,and
askedwhetherwewouldliketoparticipate.
Who could refuse?! Thanks to Lyudmila’s
and Ivan’s energy, devotion and organiza-
tionalskills,theconferencesprangintobe-
ing, the money for it materialized thanks
to some magic tricks (and to the generosity of the Swedish Research Council and
Wenner–Gren Foundations and to the help of the research network for Operator
algebras and Dynamics supported by NordForsk), mathematicians from all over
the world were invited, the topics and schedule of the talks were agreed, accom-
modation was found, and, most importantly, the time and place for the football
match of the year was arranged.
Theconferencewentverysmoothly:theweatherwasnicelyarranged–sunny
and warm, but not too hot; the speakers delivered their talks with great gusto;
the audience listened enthusiastically, asked respectful and clever questions and
applauded at the end. Finally, the organizers laid on a delicious dinner for the