Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology: Ronald G. Douglas Memorial Volume

531 Pages·2020·7.329 MB·English

by  Raul E. Curto, William Helton, Huaxin Lin, Xiang Tang , Rongwei Yang, Guoliang Yu

Operator Theory
Advances and Applications
278
Raul E. Curto, William Helton,
Huaxin Lin, Xiang Tang,
Rongwei Yang, Guoliang Yu,
Editors
Operator Theory,
Operator Algebras
and Their Interactions
with Geometry and
Topology
Ronald G. Douglas Memorial Volume

OperatorTheory: Advances andApplications
Volume278
Foundedin1979byIsraelGohberg
SeriesEditors:
JosephA.Ball(Blacksburg,VA,USA)
AlbrechtBöttcher(Chemnitz,Germany)
HarryDym(Rehovot,Israel)
HeinzLanger(Wien,Austria)
ChristianeTretter(Bern,Switzerland)
AssociateEditors: HonoraryandAdvisoryEditorialBoard:
VadimAdamyan(Odessa,Ukraine) LewisA.Coburn(Buffalo,NY,USA)
WolfgangArendt(Ulm,Germany) CiprianFoias(CollegeStation,TX,USA)
B.MalcolmBrown(Cardiff,UK) J.WilliamHelton(SanDiego,CA,USA)
RaulE.Curto(Iowa,IA,USA) MarinusA.Kaashoek(Amsterdam,NL)
KennethR.Davidson(Waterloo,ON,Canada) ThomasKailath(Stanford,CA,USA)
FritzGesztesy(Waco,TX,USA) PeterLancaster(Calgary,Canada)
PavelKurasov(Stockholm,Sweden) PeterD.Lax(NewYork,NY,USA)
VernPaulsen(Houston,TX,USA) BerndSilbermann(Chemnitz,Germany)
MihaiPutinar(SantaBarbara,CA,USA) HaroldWidom(SantaCruz,CA,USA)
IlyaSpitkovsky(AbuDhabi,UAE)
Subseries
LinearOperatorsandLinearSystems
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DanielAlpay(Orange,CA,USA)
BirgitJacob(Wuppertal,Germany)
AndréC.M.Ran(Amsterdam,TheNetherlands)
Subseries
AdvancesinPartialDifferentialEquations
Subserieseditors:
Bert-WolfgangSchulze(Potsdam,Germany)
MichaelDemuth(Clausthal,Germany)
JeromeA.Goldstein(Memphis,TN,USA)
NobuyukiTose(Yokohama,Japan)
IngoWitt(Göttingen,Germany)
Moreinformationaboutthisseriesathttp://www.springer.com/series/4850
Raul E. Curto (cid:129) William Helton (cid:129) Huaxin Lin (cid:129)
Xiang Tang (cid:129) Rongwei Yang (cid:129) Guoliang Yu
Editors
Operator Theory, Operator
Algebras and Their
Interactions with Geometry
and Topology
Ronald G. Douglas Memorial Volume
Editors
RaulE.Curto WilliamHelton
Mathematics DepartmentofMathematics
UniversityofIowa UniversityofCaliforniaSanDiego
IowaCity,IA,USA LaJolla,CA,USA
HuaxinLin XiangTang
DepartmentofMathematics DepartmentofMathematics
UniversityofOregon WashingtonUniversityinSt.Louis
Eugene,OR,USA St.Louis,MO,USA
RongweiYang GuoliangYu
MathematicsDepartment DepartmentofMathematics
UniversityofAlbany TexasA&MUniversity
Albany,NY,USA CollegeStation,TX,USA
ISSN0255-0156 ISSN2296-4878 (electronic)
OperatorTheory:AdvancesandApplications
ISBN978-3-030-43379-6 ISBN978-3-030-43380-2 (eBook)
https://doi.org/10.1007/978-3-030-43380-2
MathematicsSubjectClassification:47-XX
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Preface
TheIWOTA 2018was held atEast ChinaNormalUniversity,ShanghaifromJuly
23–27. To honor Ronald G. Douglas’ expansive and profound contributions to
mathematics,inparticularhismonumentalcontributiontooperatortheoryresearch
in China forthe past30 years,the organizershadplannedto take this occasionto
celebrate his 80th birthday. Sadly, Ron passed away at Brazos Valley Hospice in
Bryan,TexasonFebruary27.TheorganizersthusdecidedtomakethisProceeding
of IWOTA 2018 a special memorial volume. In addition to papers pertinent to
the themes of the conference, this volume collected papers from some of his
collaboratorsandformerstudents.Includedalso isan articleby physicistMichael
R.Douglaswhichgivesapersonalaccountofhisfather’sinfluence.
RonwasbornonDecember10,1938inOsgood,Indiana.Heearnedhisdoctorate
at Louisiana State University in 1962. His first paper was in measure theory and
it was published in 1964 by Michigan Mathematical Journal. Ron’s early career
research centered mostly aroundclassical operator theory topics such as invariant
∗
subspaces,Toeplitzoperators,operatormodeltheory,andC -algebras,andhesoon
emerged as one of the leaders in these fields. But in Ron’s view, there is indeed
no fence within mathematics. His work on operator theory extended naturally to
complexgeometry.ThedefinitionofCowen–Douglasoperatorwasannouncedata
symposiumatWilliamstown,Massachusettsin1975.Thisnotionmadeitpossible
to use geometric toolssuch as holomorphicbundle and curvatureto study unitary
equivalenceofoperators.ThefoundationofBrown–Douglas–Fillmoretheorywas
laid in a 1977 joint paper. Although its original intention was to use topological
methods to classify essentially normal operators, it in fact gave a simple analytic
versionofK-homology.Thisworkturnedouttobefundamentaltononcommutative
geometry and topology. His later work focused mainly on multivariable operator
theoryandinparticularitsanalyticframeworkHilbertmodulesinfunctionspaces.
The notion of Hilbert module was announced in a conference at Timis¸oara and
Herculane, Romania in 1984. In response to Shunhua Sun’s invitation, Ron gave
a series of lectures on this topic at Sichuan University, China in 1985. A more
extensivetreatmentwaslatercarriedoutinabookcoauthoredwithV.I.Paulsenin
1989.Thisframeworkgreatlypropelledthedevelopmentofmultivariableoperator
vii
viii Preface
theory. A difficult problem in this field is the Arveson–Douglasconjecture which
connects essentially normal Hilbert modules with algebraic geometry, differential
equations,indextheory,andK-homology.
Each of Ron’s aforementionedvisionarywork has nurtureda large community
of scholars. This volume containsa number of papersand surveysin these fields.
Inthisregard,itservesasa testimonythatRon’smathematicalideasare stillvery
muchalive.Inclosing,wewouldliketothankthecontributorstothisvolumeandthe
manyunnamedreviewersofthearticles.SpecialthanksgotoHuaxinLin,Guoliang
Yu,thelocalorganizersXiaomanChen,KunyuGuo,QinWang,Yi-JunYao,andthe
manyvolunteerhelpersfromEastChinaNormalUniversityandFudanUniversity,
without whom this grand scale conference would not have been possible. This
IWOTA2018isalsoindebtedtoEastChinaNormalUniversity,FudanUniversity,
and the U.S. National Science Foundation(award no. 1800780)for their financial
support.
St.Louis,MO,USA XiangTang
Albany,NY,USA RongweiYang
January28,2020
Contents
FollowingintheFootstepsofRonaldG.Douglas............................. 1
MichaelR.Douglas
FunctionalModelsforCommutingHilbert-SpaceContractions........... 11
JosephA.BallandHaripadaSau
TheExtendedAluthgeTransform.............................................. 55
ChafiqBenhidaandRaulE.Curto
OpenProblemsinWaveletTheory............................................. 77
MarcinBownikandZiemowitRzeszotnik
WhenIsEveryQuasi-MultiplieraMultiplier?............................... 101
LawrenceG.Brown
IsomorphisminWaveletsII..................................................... 111
XingdeDai,WeiHuang,andZhongyanLi
Nevanlinna-PickFamiliesandSingularRationalVarieties ................. 129
KennethR.DavidsonandEliShamovich
OnCertainCommutingIsometries, JointInvariantSubspaces
andC∗-Algebras ................................................................. 147
B.KrishnaDas,RamlalDebnath,andJaydebSarkar
SpectralAnalysis,ModelTheoryandApplicationsofFinite-Rank
Perturbations..................................................................... 171
DaleFrymarkandConstanzeLiaw
InvarianceoftheEssentialSpectraofOperatorPencils..................... 203
H.Gernandt,N.Moalla,F.Philipp,W.Selmi,andC.Trunk
DecompositionoftheTensorProductofTwoHilbertModules............. 221
SoumitraGharaandGadadharMisra
ix