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 © Springer Basel 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.birkhauser-science.com) 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