Products of Sequence Spaces

Buntinas, Martin

doi:10.1524/anly.1987.7.34.293

Cited by 11 publications

(24 citation statements)

References 3 publications

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“…Then (l) implies (2) and (2) is equivalent to (3). If<p is dense in X, the three conditions are equivalent.…”

Section: Basis and The Wilansky Propertymentioning

confidence: 98%

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Basis in Banach space, strictly cosingular maps, and the Wilansky property

Snyder¹,

Stoudt²

1991

Analysis

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A BK space Z is said to have the Wilansky property if X = Z whenever X is a BK space dense in Z with the same ^-dual as Z. The property is first formulated as a characteristic of a particular basis for a Banach space. Specifically, a basis {z"} for Z has the Wilansky property if dim Z/Y < oo whenever V is a BZ space satisfying the following: X = Z \{ X \s 3. BZ space such that Y Q X Q Z and {zn } is basic in X. It is shown that the basis {z" } for Z has the Wilansky property if and only if for each bounded block basic sequence {b"} the map A -> EA"6" of £1 into Z is strictly cosingular. The property is thus exhibited by any basis for a reflexive space. It is shown that the Wilansky property implies the absence of a copy of ti but not conversely.

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“…Then (l) implies (2) and (2) is equivalent to (3). If<p is dense in X, the three conditions are equivalent.…”

Section: Basis and The Wilansky Propertymentioning

confidence: 98%

“…Brought to you by | University of Pennsylvania Authenticated Download Date | 6/17/15 10:19 PM Details of BK products in a more general setting may be found in for instance [3]. In particular, X®Y is the smallest BK space containing all products xy = {x"y"}, XGX, yeY.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Basis in Banach space, strictly cosingular maps, and the Wilansky property

Snyder¹,

Stoudt²

1991

Analysis

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“…For E, F FK-spaces the FK product E ⊗F was introduced by Buntinas and Goes in [4] where it was shown to be the smallest FK-space containing EF = {xy : x ∈ E, y ∈ F }. An alternate characterization was given by Buntinas in [3].…”

Section: Notation and Terminologymentioning

confidence: 99%

FK-multiplier spaces

Fleming

Magee

1997

Proc. Amer. Math. Soc.

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“…The FF-product E®F of two FF-spaces F and F was defined in [6] and [7] and was characterized as the smallest FF-space containing the coordinate product E • F. If F and F are FF-spaces, then E<g>F turns out to be a FF-space. …”

Section: The Solid Hull Of An Ff-spacementioning

confidence: 99%

Absolute boundedness and absolute convergence in sequence spaces

Buntinas¹,

Tanović-Miller²

1991

Proc. Amer. Math. Soc.

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Abstract.Let ft* be the set of all sequences h = (hk)k*Ax of Os and Is. A sequence x in a topological sequence space E has the property of absolute boundedness \AB\ if ft* • x = {y\yk = hkxk , h € ft*} is a bounded subset of E . The subspace E,AB, of all sequences with absolute boundedness in E has a natural topology stronger than that induced by E. A sequence x has the property of absolute sectional convergence \AK\ if, under this stronger topology, the net {h • x} converges to x , where h ranges over all sequences in ft* with a finite number of Is ordered coordinatewise (h1 < h" iff V/c, hk < hk ). Absolute boundedness and absolute convergence are investigated. It is shown that, for an F.K-space E, we have E = E,AB, if and only if E = l°° • E, and every element of E has the property \AK\ if and only if E = c0 • E . Solid hulls and largest solid subspaces of sequence spaces are also considered. The results are applied to standard sequence spaces, convergence fields of matrix methods, classical Banach spaces of Fourier series and to more recently introduced spaces of absolutely and strongly convergent Fourier series.

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Products of Sequence Spaces

Cited by 11 publications

References 3 publications

Basis in Banach space, strictly cosingular maps, and the Wilansky property

Basis in Banach space, strictly cosingular maps, and the Wilansky property

FK-multiplier spaces

Absolute boundedness and absolute convergence in sequence spaces

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