Compact AC-operators

Ian Doust; Byron Walden

Studia Mathematica (1996)

  • Volume: 117, Issue: 3, page 275-287
  • ISSN: 0039-3223

Abstract

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We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

How to cite

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Doust, Ian, and Walden, Byron. "Compact AC-operators." Studia Mathematica 117.3 (1996): 275-287. <http://eudml.org/doc/216256>.

@article{Doust1996,
abstract = {We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.},
author = {Doust, Ian, Walden, Byron},
journal = {Studia Mathematica},
keywords = {AC-operators; compact -operators; disjoint projections; compact normal operators},
language = {eng},
number = {3},
pages = {275-287},
title = {Compact AC-operators},
url = {http://eudml.org/doc/216256},
volume = {117},
year = {1996},
}

TY - JOUR
AU - Doust, Ian
AU - Walden, Byron
TI - Compact AC-operators
JO - Studia Mathematica
PY - 1996
VL - 117
IS - 3
SP - 275
EP - 287
AB - We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.
LA - eng
KW - AC-operators; compact -operators; disjoint projections; compact normal operators
UR - http://eudml.org/doc/216256
ER -

References

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  1. [BDG] E. Berkson, I. Doust and T. A. Gillespie, Properties of AC-operators, preprint. Zbl0907.47030
  2. [BG] E. Berkson and T. A. Gillespie, Absolutely continuous functions of two variables and well-bounded operators, J. London Math. Soc (2) 30 (1984), 305-321. Zbl0537.47017
  3. [CD] Q. Cheng and I. Doust, Well-bounded operators on nonreflexive Banach spaces, Proc. Amer. Math. Soc., to appear. 
  4. [DdL] I. Doust and R. deLaubenfels, Functional calculus, integral representations, and Banach space geometry, Quaestiones Math. 17 (1994), 161-171. 
  5. [DQ] I. Doust and B. Qiu, The spectral theorem for well-bounded operators, J. Austral. Math. Soc. Ser. A 54 (1993), 334-351. Zbl0801.47022
  6. [Dow] H. R. Dowson, Spectral Theory of Linear Operators, London Math. Soc. Monographs 12, Academic Press, London, 1978. Zbl0384.47001
  7. [R] J. R. Ringrose, On well-bounded operators, J. Austral. Math. Soc. Ser. A 1 (1960), 334-343. Zbl0104.08902
  8. [Sm] D. R. Smart, Conditionally convergent spectral expansions, ibid. 1 (1960), 319-333. Zbl0104.08901

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