Copies of 
                
                  
                
                $$c_0(\Gamma )$$
                
                  
                    
                      
                        c
                        0
                      
                      
                        (
                        Γ
                        )
                      
                    
                  
                
               in the space of bounded linear operators

Pérez, Sergio A.; Rincón‐Villamizar, Michael A.

doi:10.1007/s00013-018-01296-0

Cited by 1 publication

(4 citation statements)

References 13 publications

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“…Later, Kalton and Feder extended the Bessaga-Pe lczyński result for L(X, Y ) by showing that if X is an infinite-dimensional Banach space, then c 0 ֒→ L(X, Y ) iff ℓ ∞ ֒→ L(X, Y ) [18,13]. Inspired by these results, the first and second author in [24] studied when L(X, Y ) contains (complemented) copies of c 0 (Γ) or ℓ ∞ (Γ) for an arbitrary set Γ.…”

Section: Introductionmentioning

confidence: 94%

“…Before to continue, we recall that a Banach space E has the JN Γ -property if there is a family (x * γ ) γ∈Γ in E * such that ∥x * γ ∥ = 1 for all γ ∈ Γ and (x * γ (x)) γ∈Γ ∈ c 0 (Γ) for each x ∈ E (see [24]).…”

Section: Embedding C0(γ) and ℓ∞(γ) In Banach Spaces Of Homogeneous Po...mentioning

confidence: 99%

“…Remark 3.4. Let X and Y be Banach spaces and n ∈ N. By following [14] and [24], it is not difficult to prove the following statements about the embeddability of ℓ ∞ (Γ) in either P( n X, Y ) or P w * ( n X * , Y ):…”

Section: Embedding C0(γ) and ℓ∞(γ) In Banach Spaces Of Homogeneous Po...mentioning

confidence: 99%

“…, where ˆ n,s,π X is the n-fold projective symmetric tensor product of X (see [27]), the non-trivial implication of (1.1) follows from [24,Theorem 1.1]. Note also that (1.2) follows from definitions.…”

Section: Introductionmentioning

confidence: 99%

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Embedding c0(Γ) and ℓ∞(Γ) in Banach spaces of homogeneous polynomials

Rincón,

Pérez,

Reyes

2023

Preprint

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We study Pw∗ (nX∗, Y), the Banach space of all n−homogeneous polynomials which are w∗ −w−continuous, endowed with the sup norm. The following facts are proved: (1) c0(Γ) embeds in Pw∗ (nX∗, Y ) iff either ℓ∞(Γ) embeds in Pw∗ (nX∗, Y ) or c0(Γ) embeds in the sum X ⊕ Y. (2) If c0(Γ) is isomorphic to a complemented subspace of Pw∗ (nX∗, Y ), then c0(Γ) embeds in X ⊕ Y . We also extend some linear techniques in order to embed complementably c0(Γ) in either Pw∗ (nX∗, Y ) or P(nX, Y), the Banach space of all n−homogeneous polynomials from X to Y , endowed with the sup norm. Finally, if Pw∗K(nX∗, Y) is the closed subspace of all compact polynomials in Pw∗ (nX∗, Y), we prove that ℓ∞ embeds in Pw∗K (nX∗, Y) iff ℓ∞embeds in either X or Y . As a consequence, we prove that if c0 embeds in Pw∗K(nX∗, Y), then Pw∗K(nX∗, Y ) = nX∗ (nX∗, Y) iff only one of the following statements is true: (1) c0 embeds in Y and X has the Schur property, (2) c0 embeds in X and Y has the Schur property. 2020 Mathematics Subject Classification. 46B03, 46B25, 46E40, 46G25.

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Section: Introductionmentioning

confidence: 94%

Section: Embedding C0(γ) and ℓ∞(γ) In Banach Spaces Of Homogeneous Po...mentioning

confidence: 99%

Section: Embedding C0(γ) and ℓ∞(γ) In Banach Spaces Of Homogeneous Po...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Embedding c0(Γ) and ℓ∞(Γ) in Banach spaces of homogeneous polynomials

Rincón,

Pérez,

Reyes

2023

Preprint

View full text Add to dashboard Cite

show abstract

Copies of $$c_0(\Gamma )$$ c 0 ( Γ ) in the space of bounded linear operators

Cited by 1 publication

References 13 publications

Embedding c0(Γ) and ℓ∞(Γ) in Banach spaces of homogeneous polynomials

Embedding c0(Γ) and ℓ∞(Γ) in Banach spaces of homogeneous polynomials

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