# A Borel extension approach to weakly compact operators on ${C}_{0}\left(T\right)$

Czechoslovak Mathematical Journal (2002)

- Volume: 52, Issue: 1, page 97-115
- ISSN: 0011-4642

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topPanchapagesan, Thiruvaiyaru V.. "A Borel extension approach to weakly compact operators on $C_0(T)$." Czechoslovak Mathematical Journal 52.1 (2002): 97-115. <http://eudml.org/doc/30688>.

@article{Panchapagesan2002,

abstract = {Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u\: C_0(T) \rightarrow X$ to be weakly compact.},

author = {Panchapagesan, Thiruvaiyaru V.},

journal = {Czechoslovak Mathematical Journal},

keywords = {convex Hausdorff space; Borel extension theorem; weakly compact operator},

language = {eng},

number = {1},

pages = {97-115},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A Borel extension approach to weakly compact operators on $C_0(T)$},

url = {http://eudml.org/doc/30688},

volume = {52},

year = {2002},

}

TY - JOUR

AU - Panchapagesan, Thiruvaiyaru V.

TI - A Borel extension approach to weakly compact operators on $C_0(T)$

JO - Czechoslovak Mathematical Journal

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 52

IS - 1

SP - 97

EP - 115

AB - Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u\: C_0(T) \rightarrow X$ to be weakly compact.

LA - eng

KW - convex Hausdorff space; Borel extension theorem; weakly compact operator

UR - http://eudml.org/doc/30688

ER -

## References

top- Vector Measures, Survey No.15, Amer. Math. Soc., Providence, RI., 1977. (1977) MR0453964
- Vector Measures, Pergamon Press, New York, 1967. (1967) MR0206190
- On vector measures, Proc. London Math. Soc. 17 (1967), 505–512. (1967) MR0214722
- A simple proof of the Borel extension theorem and weak compactness of operators, (to appear). (to appear) MR1940050
- Functional Analysis, Theory and Applications, Holt, Rinehart and Winston, New York, 1965. (1965) Zbl0182.16101MR0221256
- 10.4153/CJM-1953-017-4, Canad. J. Math. 5 (1953), 129–173. (1953) MR0058866DOI10.4153/CJM-1953-017-4
- Measure Theory, Van Nostrand, New York, 1950. (1950) Zbl0040.16802MR0033869
- Characterizations of Fourier-Stieltjes transform of vector and operator valued measures, Czechoslovak Math. J. 17 (1967), 261–277. (1967) MR0230872
- On complex Radon measures I, Czechoslovak Math. J. 42 (1992), 599–612. (1992) Zbl0795.28009MR1182191
- On complex Radon measures II, Czechoslovak Math. J. 43 (1993), 65–82. (1993) Zbl0804.28007MR1205231
- 10.1006/jmaa.1997.5589, J. Math. Anal. Appl. 214 (1997), 89–101. (1997) MR1645515DOI10.1006/jmaa.1997.5589
- Baire and $\sigma $-Borel characterizations of weakly compact sets in $M\left(T\right)$, Trans. Amer. Math. Soc. (1998), 4539–4547. (1998) Zbl0946.28008MR1615946
- Characterizations of weakly compact operators on ${C}_{0}\left(T\right)$, Trans. Amer. Math. Soc. (1998), 4549–4567. (1998) Zbl0906.47021
- On the limitations of the Grothendieck techniques, (to appear). (to appear) MR1865743
- 10.1112/plms/s3-19.1.89, Proc. London Math. Soc. 19 (1969), 89–106. (1969) Zbl0167.14503MR0239039DOI10.1112/plms/s3-19.1.89
- 10.5802/aif.352, Ann. Inst. Fourier (Grenoble) 20 (1970), 55–191. (1970) MR0463396DOI10.5802/aif.352

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