Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability
Keyword(s):
In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.
2005 ◽
Vol 72
(2)
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pp. 299-315
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2001 ◽
Vol 33
(4)
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pp. 443-453
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1988 ◽
Vol 103
(3)
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pp. 497-502
2011 ◽
Vol 53
(3)
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pp. 443-449
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