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Strictly Cyclic Incidence Operator Algebras
Author(s) -
Froelich John
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/49.3.502
Subject(s) - nest algebra , mathematics , pure mathematics , automorphism , hilbert space , operator algebra , class (philosophy) , interior algebra , operator (biology) , algebra over a field , non associative algebra , algebra representation , computer science , chemistry , biochemistry , repressor , transcription factor , gene , artificial intelligence
We introduce Hilbert algebras I ( P , w ) as analogues of the combinatorial incidence algebras of Doubilet, Rota and Stanley. This leads to interesting Banach algebra contexts in which to view certain important combinatorial functions such as the zeta and Möbius functions. The automorphisms and derivations of these Hilbert algebras are completely described. The algebras I ( P , w ) are used to construct a broad new class of reflexive strictly cyclic operator algebras on Hilbert space.