# Compactness of Bochner representable operators on Orlicz spaces

Compactness of Bochner representable operators on Orlicz spaces We study compactness properties of linear operators from an Orlicz space L Φ provided with a natural mixed topology $$\gamma_{L^{\Phi}}$$ to a Banach space (X, || · || X ). We derive that every Bochner representable operator $$T : L^\Phi \rightarrow X$$ is $$(\gamma_{L^{\Phi}}, || \centerdot ||_X)$$ -compact. In particular, it is shown that every Bochner representable operator $$T : L^\infty \rightarrow X$$ is (τ(L ∞, L 1), || · || X )-compact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Compactness of Bochner representable operators on Orlicz spaces

, Volume 13 (1) – Aug 9, 2008
7 pages

/lp/springer_journal/compactness-of-bochner-representable-operators-on-orlicz-spaces-mc20eEvV0G
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2179-x
Publisher site
See Article on Publisher Site

### Abstract

We study compactness properties of linear operators from an Orlicz space L Φ provided with a natural mixed topology $$\gamma_{L^{\Phi}}$$ to a Banach space (X, || · || X ). We derive that every Bochner representable operator $$T : L^\Phi \rightarrow X$$ is $$(\gamma_{L^{\Phi}}, || \centerdot ||_X)$$ -compact. In particular, it is shown that every Bochner representable operator $$T : L^\infty \rightarrow X$$ is (τ(L ∞, L 1), || · || X )-compact.

### Journal

PositivitySpringer Journals

Published: Aug 9, 2008

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