# Some characterizations of almost limited operators

Some characterizations of almost limited operators In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator $$T:X\rightarrow E$$ T : X → E from a Banach space X into a $$\sigma$$ σ -Dedekind complete Banach lattice E is almost limited if and only if $$\left\| T^{*}\left( f_{n}\right) \right\| \rightarrow 0$$ T ∗ f n → 0 for every positive weak $$^{*}$$ ∗ null sequence $$\left( f_{n}\right)$$ f n of $$E^{*}$$ E ∗ . Moreover, we present some interesting connections between almost limited, almost Dunford–Pettis and limited operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Some characterizations of almost limited operators

, Volume 21 (3) – Jul 21, 2016
10 pages

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
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/s11117-016-0437-x
Publisher site
See Article on Publisher Site

### Abstract

In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator $$T:X\rightarrow E$$ T : X → E from a Banach space X into a $$\sigma$$ σ -Dedekind complete Banach lattice E is almost limited if and only if $$\left\| T^{*}\left( f_{n}\right) \right\| \rightarrow 0$$ T ∗ f n → 0 for every positive weak $$^{*}$$ ∗ null sequence $$\left( f_{n}\right)$$ f n of $$E^{*}$$ E ∗ . Moreover, we present some interesting connections between almost limited, almost Dunford–Pettis and limited operators.

### Journal

PositivitySpringer Journals

Published: Jul 21, 2016

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