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1
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Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces

100%
Dineen S.
Studia Mathematica
|
1995
|
tom 113
|
nr 1
43-54
EN
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2, 4, 5, 6] - together with new examples, e.g. Banach spaces with an unconditional finite-dimensional Schauder decomposition and certain Fréchet-Schwartz spaces. This gives the first examples of Fréchet spaces, which are not nuclear, with τ_{0} = τ_{δ} on H(E).
2
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Convexity in complex analysis

100%
Dineen S.
Banach Center Publications
|
1995
|
tom 31
|
nr 1
151-162
3
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Distances between Hilbertian operator spaces

64%
Dineen S., Radu C.
Studia Mathematica
|
2014
|
tom 222
|
nr 1
29-39
EN
We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.
4
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Invertibility in tensor products of Q-algebras

64%
Dineen S., Sevilla-Peris P.
Studia Mathematica
|
2002
|
tom 153
|
nr 3
269-284
EN
We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.
5
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The density property for JB*-triples

51%
Dineen S., Mackey M., Mellon P.
Studia Mathematica
|
1999
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tom 137
|
nr 2
143-160
EN
We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.
6
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Analytic functionals on fully nuclear spaces

26%
Dineen S.
Studia Mathematica
|
1982
|
tom 73
|
nr 1
11-32
7
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Holomorphy types on a Banach spaces

26%
Dineen S.
Studia Mathematica
|
1971
|
tom 39
|
nr 3
241-288
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