Processing math: 0%

Wykorzystujemy pliki cookies aby ułatwić Ci korzystanie ze strony oraz w celach analityczno-statystycznych.

A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Bimodules over , harmonic operators and the non-commutative Poisson boundary

Volume 249 / 2019

M. Anoussis, A. Katavolos, I. G. Todorov Studia Mathematica 249 (2019), 193-213 MSC: Primary 43A20, 22D15; Secondary 22D25, 43A77, 47L05. DOI: 10.4064/sm180313-6-9 Published online: 7 June 2019

Abstract

Starting with a left ideal J of L^1(G) we consider its annihilator J^{\perp } in L^{\infty }(G) and the generated \mathop {\rm VN}\nolimits (G)-bimodule in \mathcal {B}(L^2(G)), \mathop {\rm Bim}\nolimits (J^{\perp }). We prove that \mathop {\rm Bim}\nolimits (J^{\perp })=(\mathop {\rm Ran}\nolimits J)^{\perp } when G is weakly amenable discrete, compact or abelian, where \mathop {\rm Ran}\nolimits J is a suitable saturation of J in the trace class. We define jointly harmonic functions and jointly harmonic operators and show that, for these classes of groups, the space of jointly harmonic operators is the \mathop {\rm VN}\nolimits (G)-bimodule generated by the space of jointly harmonic functions. Using this, we give a proof of the following result of Izumi and Ja\-wor\-ski–Neufang: the non-commutative Poisson boundary is isomorphic to the crossed product of the space of harmonic functions by G.

Authors

  • M. AnoussisDepartment of Mathematics
    University of the Aegean
    Samos 83 200, Greece
    e-mail
  • A. KatavolosDepartment of Mathematics
    University of Athens
    Athens 157 84, Greece
    e-mail
  • I. G. TodorovMathematical Sciences Research Centre
    Queen’s University Belfast
    Belfast BT7 1NN, United Kingdom
    and
    School of Mathematical Sciences
    Nankai University
    300071 Tianjin, China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image