# Compactness of the integration operator associated with a vector measure

S. Okada; W. J. Ricker; L. Rodríguez-Piazza

Studia Mathematica (2002)

- Volume: 150, Issue: 2, page 133-149
- ISSN: 0039-3223

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topS. Okada, W. J. Ricker, and L. Rodríguez-Piazza. "Compactness of the integration operator associated with a vector measure." Studia Mathematica 150.2 (2002): 133-149. <http://eudml.org/doc/285203>.

@article{S2002,

abstract = {A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.},

author = {S. Okada, W. J. Ricker, L. Rodríguez-Piazza},

journal = {Studia Mathematica},

keywords = {vector measure; variation; integration operator; compact operator},

language = {eng},

number = {2},

pages = {133-149},

title = {Compactness of the integration operator associated with a vector measure},

url = {http://eudml.org/doc/285203},

volume = {150},

year = {2002},

}

TY - JOUR

AU - S. Okada

AU - W. J. Ricker

AU - L. Rodríguez-Piazza

TI - Compactness of the integration operator associated with a vector measure

JO - Studia Mathematica

PY - 2002

VL - 150

IS - 2

SP - 133

EP - 149

AB - A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.

LA - eng

KW - vector measure; variation; integration operator; compact operator

UR - http://eudml.org/doc/285203

ER -

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