Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

Weak Containment and Weak Frobenius Reciprocity

Elliot C. Gootman
Proceedings of the American Mathematical Society
Vol. 54, No. 1 (Jan., 1976), pp. 417-422
DOI: 10.2307/2040832
Stable URL: http://www.jstor.org/stable/2040832
Page Count: 6

You can always find the topics here!

Topics: Topological theorems, Mathematical theorems, Second countable spaces, Algebra
Were these topics helpful?
See somethings inaccurate? Let us know!

Select the topics that are inaccurate.

Cancel
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Weak Containment and Weak Frobenius Reciprocity
Preview not available

Abstract

We study weak containment relations between unitary representations of a group G and a closed normal subgroup K by exploiting a property of G-ergodic quasi-invariant measures on the primitive ideal space of K. By this means, we prove that every irreducible representation of G is weakly contained in a representation induced from an irreducible representation of K if the quotient group G/K is amenable; and that the pair (G, K) satisfies a weak Frobenius reciprocity property if and only if G/K is amenable and G acts minimally on the primitive ideal space of K. If G/K is compact, G acts minimally if and only if the primitive ideal space of K is T1.

Page Thumbnails

  • Thumbnail: Page 
417
    417
  • Thumbnail: Page 
418
    418
  • Thumbnail: Page 
419
    419
  • Thumbnail: Page 
420
    420
  • Thumbnail: Page 
421
    421
  • Thumbnail: Page 
422
    422