Located operators

B.A.W. Spitters

doi:10.1002/1521-3870(200210)48:1+<107::AID-MALQ107>3.0.CO;2-O

Located operators

B.A.W. Spitters

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

3 Citaten (Scopus)

Samenvatting

We study operators with located graph in Bishop-style constructive mathematics. It is shown that a bounded operator has an adjoint if and only if its graph is located. Locatedness of the graph is a necessary and sufficient condition for an unbounded normal operator to have a spectral decomposition. These results suggest that located operators are the right generalization of bounded operators with an adjoint.

Originele taal-2	Engels
Pagina's (van-tot)	107-122
Tijdschrift	Mathematical Logic Quarterly
Volume	48
Nummer van het tijdschrift	S1
DOI's	https://doi.org/10.1002/1521-3870(200210)48:1+<107::AID-MALQ107>3.0.CO;2-O
Status	Gepubliceerd - 2002

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10.1002/1521-3870(200210)48:1+<107::AID-MALQ107>3.0.CO;2-O

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abstract = "We study operators with located graph in Bishop-style constructive mathematics. It is shown that a bounded operator has an adjoint if and only if its graph is located. Locatedness of the graph is a necessary and sufficient condition for an unbounded normal operator to have a spectral decomposition. These results suggest that located operators are the right generalization of bounded operators with an adjoint.",

author = "B.A.W. Spitters",

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AB - We study operators with located graph in Bishop-style constructive mathematics. It is shown that a bounded operator has an adjoint if and only if its graph is located. Locatedness of the graph is a necessary and sufficient condition for an unbounded normal operator to have a spectral decomposition. These results suggest that located operators are the right generalization of bounded operators with an adjoint.

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Located operators

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