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Triangular Algebras and Ideals of Nest Algebras
John Lindsay Orr
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Memoirs of the American Mathematical Society
1995; 49 pp; softcover
Volume: 117
ISBN-10: 0-8218-0405-7
ISBN-13: 978-0-8218-0405-6
List Price: US$32
Individual Members: US$19.20
Institutional Members: US$25.60
Order Code: MEMO/117/562
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Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras.

In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.

Readership

Graduate students and research mathematicians, particularly those specializing in operator theory and/or operator algebras.

Table of Contents

  • Introduction
  • The diagonal seminorm function
  • The interpolation theorem
  • Maximal off-diagonal ideals
  • Maximal triangular algebras
  • Compressible maximal triangular algebras
  • References
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