Weak compactness in the dual space of a C*-algebra

C. A. Akemann; P. G. Dodds; J. L.B. Gamlen

doi:10.1016/0022-1236(72)90040-7

Weak compactness in the dual space of a C^*-algebra

C. A. Akemann, P. G. Dodds, J. L.B. Gamlen

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

40 Citations (Scopus)

Abstract

Several results in noncommutative measure theory for C^*-algebras are proved. A bounded linear map from a C^*-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}_i} of states on a W^*-algebra converges weakly if it converges weak^* (Corollary 3.3).

Original language	English
Pages (from-to)	446-450
Number of pages	5
Journal	Journal of Functional Analysis
Volume	10
Issue number	4
DOIs	https://doi.org/10.1016/0022-1236(72)90040-7
Publication status	Published - Aug 1972

Bibliographical note

Funding Information:
*Partially supported by NSF grant GP 19101. + Supported in part by NRC grant A 7552.

Access to Document

10.1016/0022-1236(72)90040-7Licence: In Copyright

Cite this

@article{5a3db8bf6e124f5a898a7237d5a39055,

title = "Weak compactness in the dual space of a C*-algebra",

abstract = "Several results in noncommutative measure theory for C*-algebras are proved. A bounded linear map from a C*-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}i} of states on a W*-algebra converges weakly if it converges weak* (Corollary 3.3).",

author = "Akemann, {C. A.} and Dodds, {P. G.} and Gamlen, {J. L.B.}",

note = "Funding Information: *Partially supported by NSF grant GP 19101. + Supported in part by NRC grant A 7552.",

year = "1972",

month = aug,

doi = "10.1016/0022-1236(72)90040-7",

language = "English",

volume = "10",

pages = "446--450",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - Weak compactness in the dual space of a C*-algebra

AU - Akemann, C. A.

AU - Dodds, P. G.

AU - Gamlen, J. L.B.

N1 - Funding Information: *Partially supported by NSF grant GP 19101. + Supported in part by NRC grant A 7552.

PY - 1972/8

Y1 - 1972/8

N2 - Several results in noncommutative measure theory for C*-algebras are proved. A bounded linear map from a C*-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}i} of states on a W*-algebra converges weakly if it converges weak* (Corollary 3.3).

AB - Several results in noncommutative measure theory for C*-algebras are proved. A bounded linear map from a C*-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}i} of states on a W*-algebra converges weakly if it converges weak* (Corollary 3.3).

UR - http://www.scopus.com/inward/record.url?scp=0001006235&partnerID=8YFLogxK

U2 - 10.1016/0022-1236(72)90040-7

DO - 10.1016/0022-1236(72)90040-7

M3 - Article

AN - SCOPUS:0001006235

SN - 0022-1236

VL - 10

SP - 446

EP - 450

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

ER -

Weak compactness in the dual space of a C^*-algebra

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this