Topological characterisation of weakly compact operators

Antonio M. Peralta; Ignacio Villanueva; John David Maitland Wright; Kari Ylinen

doi:10.1016/j.jmaa.2006.02.066

Topological characterisation of weakly compact operators

Antonio M. Peralta, Ignacio Villanueva, John David Maitland Wright, Kari Ylinen

Mathematical Science

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

Let X be a Banach space. Then there is a locally convex topology for X, the "Right topology," such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the "Right" topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	968-974
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	325
Issue number	2
Early online date	23 Mar 2006
DOIs	https://doi.org/10.1016/j.jmaa.2006.02.066
Publication status	Published - 15 Jan 2007

Keywords

weakly compact operators
right topology
Mackey topology

Access to Document

10.1016/j.jmaa.2006.02.066

Cite this

@article{6a6f3c71683b422eb9d41ec0ab8148a6,

title = "Topological characterisation of weakly compact operators",

abstract = "Let X be a Banach space. Then there is a locally convex topology for X, the {"}Right topology,{"} such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the {"}Right{"} topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.",

keywords = "weakly compact operators, right topology, Mackey topology",

author = "Peralta, {Antonio M.} and Ignacio Villanueva and Wright, {John David Maitland} and Kari Ylinen",

year = "2007",

month = jan,

day = "15",

doi = "10.1016/j.jmaa.2006.02.066",

language = "English",

volume = "325",

pages = "968--974",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Topological characterisation of weakly compact operators

AU - Peralta, Antonio M.

AU - Villanueva, Ignacio

AU - Wright, John David Maitland

AU - Ylinen, Kari

PY - 2007/1/15

Y1 - 2007/1/15

N2 - Let X be a Banach space. Then there is a locally convex topology for X, the "Right topology," such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the "Right" topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.

AB - Let X be a Banach space. Then there is a locally convex topology for X, the "Right topology," such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the "Right" topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). (c) 2006 Elsevier Inc. All rights reserved.

KW - weakly compact operators

KW - right topology

KW - Mackey topology

U2 - 10.1016/j.jmaa.2006.02.066

DO - 10.1016/j.jmaa.2006.02.066

M3 - Article

VL - 325

SP - 968

EP - 974

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

Topological characterisation of weakly compact operators

Abstract

Keywords

Access to Document

Fingerprint

Cite this