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A Reflexive Space of Holomorphic Functions in Infinitely Many Variables
A Reflexive Space of Holomorphic Functions in Infinitely Many Variables,10.2307/2044483,Proceedings of The American Mathematical Society,Raymundo Alen
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A Reflexive Space of Holomorphic Functions in Infinitely Many Variables
(
Citations: 45
)
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Raymundo Alencar
,
Richard M. Aron
,
Seán Dineen
Journal:
Proceedings of The American Mathematical Society  PROC AMER MATH SOC
, vol. 90, no. 3, pp. 407407, 1984
DOI:
10.2307/2044483
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Citation Context
(19)
...Moreover, for each n, PV ( n T ∗ ) = P( n T ∗ ) and then PV ( n T ∗ ) is reflexive [
1
]...
Daniel Carando
,
et al.
Spectra of weighted algebras of holomorphic functions
...After his pioneering work, many authors considered the problem of finding necessary and sufficient condition for the space P (nE) to be reflexive (see [3], [4], [
5
], [18] and [13])...
...Alencar, Aron and Dineen showed in [
5
] that P (nT ∗) is reflexive for every n ,w hereT ∗ is the Tsirelson’s space (see [27])...
Adriano L. Aguiar
,
et al.
Reflexivity of Spaces of Polynomials on Direct Sums of Banach Spaces
...In [36], B. Tsirelson constructed a re∞exive Banach space X, with an unconditional Schauder basis, that does not contain any subspace that is isomorphic to c0 or to any lp. R. Alencar, R. Aron and S. Dineen proved in [
1
] that Pf(mX) is normdense in P(mX) for all m 2N. Inspired by this result, we will say that a Banach space E is a Tsirelsonlike space if E is re∞exive and Pf(mE) is normdense in P(mE) for all m 2N...
Daniela M. Vieira
.
Theorems of BanachStone Type for Algebras of Holomorphic Functions on...
...If 0 < r < 1, the closed ball rB is a weakly compact subset of A(B) . (This is because polynomials on X are X continuous on bounded sets, and the Taylor series of a bounded analytic function on B converges uniformly on rB; see [
AAD
], [AGL], [GLR].) Hence rB has no interpolating sequence for A(B) . However, rB is not norm compact, and consequently it contains hyperbolically separated sequences...
P. Galindo
,
et al.
Composition Operators on Uniform Algebras and the Pseudohyperbolic Met...
...Example 5.3. In [19], B. Tsirelson constructed a reflexive Banach space E, with an unconditional Schauder basis, that does not contain any subspace which is isomorphic to c0 or to any lp. R. Alencar, R. Aron and S. Dineen proved in [
1
] that Pf(mE) is dense in P(mE), for all m 2 N...
Daniela M. VIEIRA
.
Theorems of BanachStone type for algebras of holomorphic functions on...
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Citations
(45)
Mideals of homogeneous polynomials
(
Citations: 1
)
Veronica Dimant
Published in 2010.
The approximation property for spaces of holomorphic functions on infinite dimensional spaces II
(
Citations: 1
)
Seán Dineen
,
Jorge Mujica
Journal:
Journal of Functional Analysis  J FUNCT ANAL
, vol. 259, no. 2, pp. 545560, 2010
Approximation properties determined by operator ideals
Sonia Berrios
,
Geraldo Botelho
Published in 2010.
Spectra of weighted algebras of holomorphic functions
(
Citations: 1
)
Daniel Carando
,
Pablo SevillaPeris
Journal:
Mathematische Zeitschrift  MATH Z
, vol. 263, no. 4, pp. 887902, 2009
Reflexivity of Spaces of Polynomials on Direct Sums of Banach Spaces
Adriano L. Aguiar
,
Luiza A. Moraes
Journal:
Publications of The Research Institute for Mathematical Sciences  PUBL RES INST MATH SCI
, vol. 45, no. 2, pp. 351361, 2009