We develop a theory of herzschur multipliers of a c. Positive herzschur multipliers and approximation properties of crossed products volume 165 issue 3 andrew mckee, adam skalski, ivan g. Next 10 measurable schur multipliers and completely bounded multipliers. Herz and issai schur is a special kind of mapping from a group to the field of complex numbers. The multiplier was introduced by haagerup and collaborators in 1985 and it is a special kind of mapping used in the field of representation theory, from a group to the complex number field. Herzschur multipliers of university of gothenburg, sweden. Ams transactions of the american mathematical society. Herz schur multipliers and weakly almost periodic functions on locally compact groups guangwu xu abstract. Andrew mckee queens university belfast thursday 20 april 2017, 14. Citeseerx citation query herzschur multipliers and. Herzschur multipliers were named after two scientists. In joint work with haagerup, we show that a connected simple lie group has the weak haagerup property if and only if. Herzschur multiplier news newspapers books scholar jstor june 2009. Completely bounded maps in the banach space setting 9.
Clear and carefully developed, this book conveys a comprehensive picture of the current state of this subject and offers a unified treatment of a wealth of important results. During the last thirty years, much research has been devoted to the study of various properties of the second cohomology group, also known as the schur multiplier. In order to investigate the relationship between weak amenability and the haagerup property for groups, we introduce the weak haagerup property, and we prove that having this approximation property is equivalent to the existence of a semigroup of herz schur multipliers generated by. Numerous and frequentlyupdated resource results are available from this search. Herzschur multipliers of dynamical systems sciencedirect. A characterization of radial herzschur multipliers on free. We introduce schur amultipliers, establish a characterisation that generalises the classical descriptions of schur multipliers, and present a transference theorem in the new setting, identifying isometrically the herz schur multipliers of the dynamical system a, g. Uniformly bounded representations of free groups and herz schur multipliers marek bozejko on. Let g be a second countable, locally compact group and let f be a continuous herz schur multiplier on g. Herz schur multipliers and completely bounded multipliers of the fourier algebra of a locally compact group 1984 by marek bozejko, gero fendler venue.
Multipliers of dynamical systems queens university belfast. We extend the notion of a herz schur multiplier to the setting of noncommutative dynamical systems. Add to your lists download to your calendar using vcal. By continuing on this website, you approve of our use of cookies. Gr 31 aug 2009 schur multipliers and spherical functions on homogeneous trees u. Similarity problems and completely bounded maps ebook. Among the large number of applications of schur multipliers is the description of the space m cb a g of completely bounded multipliers also known as herz schur multipliers of the fourier algebra a g of a locally compact group g, introduced by j. Herzschur multipliers of dynamical systems classification of operator algebras. M0ag of the radial functions on the free non abelian. Characterizing herzschur multipliers using coefficient. Herzschur multipliers of dynamical systems nasaads.
We introduce schur a multipliers, establish a characterisation that. Introduction the notion of a schur multiplier has its origins in the work of i. Herz schur multipliers and approximation properties. For a locally compact group g and 1 herz fig atalamanca algebra andbpg the herz schur multipliers ofg, and mapg the multipliers ofapg.
A multipliers and a class of herz schur multiplier of semidire ct pro duct bundle are identi. In this short chapter, we discuss schur multipliers restricted to various subspaces e. As applications, we obtaina closed expression for the completely bounded fourier multiplier norm. Herz schur multipliers is linearly bounded by the word length function. Operatorvalued schur multipliers and herzschur multipliers of dynamical systems lyudmila turowska chalmers university of technology and university of gothenburg joint work with andrew mckeegothenburg and ivan todorov belfast banach algebras 2019 july 1118, 2019 july, 2019 july, 2019 3. Part of the lecture notes in mathematics book series lnm, volume 1618. These notes formed the basis of a series of lectures at the programme \harmonic analysis. In this short chapter, we discuss schur multipliers restricted to various subspaces \e \subset bh\. On idempotents of completely bounded multipliers of the fourier. Troels steenstrup ryszard szwarc august 31, 2009 abs. Fendler, herz schur multipliers and coefficients of bounded representations, thesis at heidelberg univ. On one hand, these can be viewed as the special class of schur multipliers whose symbol g g.
According to the bozekjkofendler theorem, a continuous function on is a completely bounded multiplier of if and only if the function on defined by is a schur multiplier. The space l1 g can, by virtue of the radonnikodym theorem, be re garded as the closed ideal of all absolutely continuous with respect to m measures in mg. We show that the schur multipliers which are completely bounded maps from e to e are closely related to the fourier multipliers on the hardy space h 1. We discuss special classes of herzschur multipliers, in particular, those associated to a locally compact abelian group g. They were considered by herz in a dual framework, as multipliers on ag before the notion of complete boundedness surfaced. Herzschur multipliers and approximation properties. Stanford libraries official online search tool for books, media, journals, databases, government documents and more. These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space bh of all bounded operators on a complex hilbert space h.
Request pdf herz schur multipliers of dynamical systems we extend the notion of herz schur multipliers to the setting of noncommutative dynamical systems. In the second half of the paper we study semigroups of radial herz schur multipliers on free groups. Positive herzschur multipliers and approximation properties of. Gilles pisier these notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space bh of all bounded operators on a complex hilbert space h. A characterization of radial herzschur multipliers on groups which are free products g. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. M0ag of the radial functions on the free nonabelian. Herzschur multipliers of dynamical systems request pdf. Picardello, harmonic analysis on free groups, lecture notes in pure and applied mathematics, vol. Instead, we focus on the development of the core material on multipliers on locally compact groups and various speci c classes of interest. Multipliers and lacunary sets in nonamenable groups. The first one deals with group representations, the second one with c algebras and the third one with the disc. Uniformly bounded representations of free groups and herz. Herzschur multiplier from wikipedia, the free encyclopedia in the mathematical field of representation theory, a herzschur multiplier named after carl s.
Moreover, there exist examples of groups that fail the first two properties but nevertheless have the weak haagerup property see 27, corollary 5. The continuous rightinvariant schur multipliers on are called herz schur multipliers. Top american libraries canadian libraries universal library community texts project gutenberg biodiversity heritage library childrens library. The similarity problem for cyclic homomorphisms on a calgebra 8. The university of gothenburg uses cookies to provide you with the best possible user experience. Furthermore, we will also introduce and study generalised schur multipliers, and derive links between these two notions which extend the classical results describing herz schur multipliers in terms of schur multipliers. This theory will be developed in as much generality as possible, with reference to the classical motivation. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Herz schur multipliers similarity problem for cyclic homomorphisms on a calgebra. Similarity problems and completely bounded maps gilles. We prove that a generator of such a semigroup is linearly bounded by the word length function.
23 757 1296 345 1020 132 1001 802 1076 1478 1019 1520 1517 296 94 648 1186 355 1313 937 536 857 11 1168 874 818 554 1308 830 638 1366 1238 156 849 882 163 184 658 1107 648 498 237 1314 507 941