Shift Оperators

Anoussis, M. S.

Serdica Mathematical Journal (2015)

  • Volume: 41, Issue: 1, page 35-48
  • ISSN: 1310-6600

Abstract

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Shift operators play an important role in different areas of Mathematics such as Operator Theory, Dynamical Systems and Complex Analysis. In these lectures we discuss basic properties of these operators. We present Beurling’s Theorem which describes the invariant subspaces of the shift. The structure of the C *-algebra generated by the shift is described. We also indicate how the shift operators appear in the analysis of isometries on a Hilbert space: Wold decomposition and Coburn’s theorem. 2010 Mathematics Subject Classification: Primary 46L05; Secondary 47A15, 47B35.

How to cite

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Anoussis, M. S.. "Shift Оperators." Serdica Mathematical Journal 41.1 (2015): 35-48. <http://eudml.org/doc/295048>.

@article{Anoussis2015,
abstract = {Shift operators play an important role in different areas of Mathematics such as Operator Theory, Dynamical Systems and Complex Analysis. In these lectures we discuss basic properties of these operators. We present Beurling’s Theorem which describes the invariant subspaces of the shift. The structure of the C *-algebra generated by the shift is described. We also indicate how the shift operators appear in the analysis of isometries on a Hilbert space: Wold decomposition and Coburn’s theorem. 2010 Mathematics Subject Classification: Primary 46L05; Secondary 47A15, 47B35.},
author = {Anoussis, M. S.},
journal = {Serdica Mathematical Journal},
keywords = {shift operator; Toeplitz algebra; Wold decomposition; invariant subspace},
language = {eng},
number = {1},
pages = {35-48},
publisher = {Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences},
title = {Shift Оperators},
url = {http://eudml.org/doc/295048},
volume = {41},
year = {2015},
}

TY - JOUR
AU - Anoussis, M. S.
TI - Shift Оperators
JO - Serdica Mathematical Journal
PY - 2015
PB - Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
VL - 41
IS - 1
SP - 35
EP - 48
AB - Shift operators play an important role in different areas of Mathematics such as Operator Theory, Dynamical Systems and Complex Analysis. In these lectures we discuss basic properties of these operators. We present Beurling’s Theorem which describes the invariant subspaces of the shift. The structure of the C *-algebra generated by the shift is described. We also indicate how the shift operators appear in the analysis of isometries on a Hilbert space: Wold decomposition and Coburn’s theorem. 2010 Mathematics Subject Classification: Primary 46L05; Secondary 47A15, 47B35.
LA - eng
KW - shift operator; Toeplitz algebra; Wold decomposition; invariant subspace
UR - http://eudml.org/doc/295048
ER -

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