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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weak and Strong Density of Compositions


Authors: Luigi De Pascale and Eugene Stepanov
Journal: Trans. Amer. Math. Soc. 352 (2000), 3707-3721
MSC (1991): Primary 47B38, 47A67, 34K05
Published electronically: March 2, 2000
MathSciNet review: 1675182
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Abstract:

The convergence in various topologies of sequences of inner superposition (composition) operators acting between Lebesgue spaces and of their linear combinations is studied. In particular, the sequential density results for the linear span of such operators is proved for the weak, weak continuous and strong operator topologies.


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Additional Information

Luigi De Pascale
Affiliation: Dipartimento di Matematica, Universitá di Pisa, via Buonarrotti 2, 56127 Pisa, Italy; Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Email: depascal@dm.unipi.it

Eugene Stepanov
Affiliation: Computer Technology Department, St. Petersburg Inst. of Fine Mechanics and Optics, 14 Sablinskaya ul., 197101 St. Petersburg, Russia

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02510-1
PII: S 0002-9947(00)02510-1
Received by editor(s): May 5, 1997
Received by editor(s) in revised form: March 11, 1998
Published electronically: March 2, 2000
Dedicated: Dedicated to N.V. Azbelev on the occasion of his 75th birthday
Article copyright: © Copyright 2000 American Mathematical Society