Compact covariance operators’

Charles R. Baker; Ian W. McKeague

doi:10.1090/S0002-9939-1981-0627699-7

Compact covariance operators’

Charles R. Baker
, Ian W. McKeague

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

Let B be a real separable Banach space and R: B*→B a covariance operator. All representations of R in the form Σe_n Φ e_n, {e_n, n > l} Є B, are characterized. Necessary and sufficient conditions for R to be compact are obtained, including a generalization of Mercer’s theorem. An application to characteristic functions is given. © 1981 American Mathematical Society.

Original language	English
Pages (from-to)	590-593
Journal	Proceedings of the American Mathematical Society
Volume	83
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1981-0627699-7
Publication status	Published - Nov 1981
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Compact operator
Covariance operator
Probability in Banach spaces

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title = "Compact covariance operators{\textquoteright}",

abstract = "Let B be a real separable Banach space and R: B*→B a covariance operator. All representations of R in the form Σen Φ en, \{en, n > l\} Є B, are characterized. Necessary and sufficient conditions for R to be compact are obtained, including a generalization of Mercer{\textquoteright}s theorem. An application to characteristic functions is given. {\textcopyright} 1981 American Mathematical Society.",

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author = "Baker, \{Charles R.\} and McKeague, \{Ian W.\}",

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year = "1981",

month = nov,

doi = "10.1090/S0002-9939-1981-0627699-7",

language = "English",

volume = "83",

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journal = "Proceedings of the American Mathematical Society",

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T1 - Compact covariance operators’

AU - Baker, Charles R.

AU - McKeague, Ian W.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 1981/11

Y1 - 1981/11

N2 - Let B be a real separable Banach space and R: B*→B a covariance operator. All representations of R in the form Σen Φ en, {en, n > l} Є B, are characterized. Necessary and sufficient conditions for R to be compact are obtained, including a generalization of Mercer’s theorem. An application to characteristic functions is given. © 1981 American Mathematical Society.

AB - Let B be a real separable Banach space and R: B*→B a covariance operator. All representations of R in the form Σen Φ en, {en, n > l} Є B, are characterized. Necessary and sufficient conditions for R to be compact are obtained, including a generalization of Mercer’s theorem. An application to characteristic functions is given. © 1981 American Mathematical Society.

KW - Compact operator

KW - Covariance operator

KW - Probability in Banach spaces

UR - https://www.scopus.com/pages/publications/84966206989

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84966206989&origin=recordpage

U2 - 10.1090/S0002-9939-1981-0627699-7

DO - 10.1090/S0002-9939-1981-0627699-7

M3 - RGC 21 - Publication in refereed journal

SN - 0002-9939

VL - 83

SP - 590

EP - 593

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Compact covariance operators’

Abstract

Bibliographical note

Research Keywords

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