Proceedings of the Centre for Mathematics and its Applications

Contractive projections on Banach spaces

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Abstract

Increasing sequences of contractive projections on a reflexive $L^p$ space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive $AC$-functional calculus is scalar-type spectral.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 50-58

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340102

Mathematical Reviews number (MathSciNet)
MR1009593

Zentralblatt MATH identifier
0687.46009

Citation

Contractive projections on Banach spaces. Workshop/Miniconference on Functional Analysis and Optimization, 50--58, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340102


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