# Strongly compact algebras.

Miguel Lacruz; Victor Lomonosov; Luis Rodríguez Piazza

RACSAM (2006)

- Volume: 100, Issue: 1-2, page 191-207
- ISSN: 1578-7303

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topLacruz, Miguel, Lomonosov, Victor, and Rodríguez Piazza, Luis. "Strongly compact algebras.." RACSAM 100.1-2 (2006): 191-207. <http://eudml.org/doc/41652>.

@article{Lacruz2006,

abstract = {An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras are established. Next, a characterization of strongly compact normal operators is provided in terms of their spectral representation, and some applications are given. Finally, necessary and sufficient conditions for a weighted shift to be strongly compact are obtained in terms of the sliding products of its weights, and further applications are derived.},

author = {Lacruz, Miguel, Lomonosov, Victor, Rodríguez Piazza, Luis},

journal = {RACSAM},

keywords = {strongly compact algebras and operators; normal operators},

language = {eng},

number = {1-2},

pages = {191-207},

title = {Strongly compact algebras.},

url = {http://eudml.org/doc/41652},

volume = {100},

year = {2006},

}

TY - JOUR

AU - Lacruz, Miguel

AU - Lomonosov, Victor

AU - Rodríguez Piazza, Luis

TI - Strongly compact algebras.

JO - RACSAM

PY - 2006

VL - 100

IS - 1-2

SP - 191

EP - 207

AB - An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras are established. Next, a characterization of strongly compact normal operators is provided in terms of their spectral representation, and some applications are given. Finally, necessary and sufficient conditions for a weighted shift to be strongly compact are obtained in terms of the sliding products of its weights, and further applications are derived.

LA - eng

KW - strongly compact algebras and operators; normal operators

UR - http://eudml.org/doc/41652

ER -

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