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Embeddings of Spaces of Holomorphic Functions of Bounded Type
Author(s) -
Ansemil J. M.,
Aron R. M.,
Ponte S.
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-46.3.482
Subject(s) - holomorphic function , mathematics , embedding , bounded function , linear subspace , banach space , quotient space (topology) , subspace topology , space (punctuation) , pure mathematics , fréchet space , quotient , type (biology) , combinatorics , discrete mathematics , interpolation space , functional analysis , mathematical analysis , computer science , ecology , biochemistry , chemistry , artificial intelligence , biology , gene , operating system
Let U be an open subset of a complex locally convex space E , let F be a closed subspace of E , and let п: E / F be the canonical quotient mapping. In this paper we study the induced mapping п ∗ , taking f ɛ H b {п( U )) → fo п ɛ H b , where H b ( V ) denotes the space of holomorphic functions of bounded type on an open set V . We prove that this mapping is an embedding when E is a Fréchet‐Schwartz space, and that it is not an embedding for certain subspaces F of every Fréchet‐Montel, not Schwartz, space. We provide several examples in the case where E is a Banach space to illustrate the sharpness of our results.