# ${w}^{*}$-basic sequences and reflexivity of Banach spaces

Czechoslovak Mathematical Journal (2005)

- Volume: 55, Issue: 3, page 677-681
- ISSN: 0011-4642

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topJohn, Kamil. "$w^*$-basic sequences and reflexivity of Banach spaces." Czechoslovak Mathematical Journal 55.3 (2005): 677-681. <http://eudml.org/doc/30977>.

@article{John2005,

abstract = {We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $\mathcal \{L\}(X,Y)$ is not reflexive for reflexive $X$ and $Y$ then $\mathcal \{L\}(X_1, Y)$ is is not reflexive for some $X_1\subset X$, $X_1$ having a basis.},

author = {John, Kamil},

journal = {Czechoslovak Mathematical Journal},

keywords = {reflexive Banach space; Schauder basis; quotient space; w$^*$-basic sequence; tensor product; reflexive Banach space; Schauder basis; quotient space; w-basic sequence; tensor product},

language = {eng},

number = {3},

pages = {677-681},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {$w^*$-basic sequences and reflexivity of Banach spaces},

url = {http://eudml.org/doc/30977},

volume = {55},

year = {2005},

}

TY - JOUR

AU - John, Kamil

TI - $w^*$-basic sequences and reflexivity of Banach spaces

JO - Czechoslovak Mathematical Journal

PY - 2005

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 55

IS - 3

SP - 677

EP - 681

AB - We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $\mathcal {L}(X,Y)$ is not reflexive for reflexive $X$ and $Y$ then $\mathcal {L}(X_1, Y)$ is is not reflexive for some $X_1\subset X$, $X_1$ having a basis.

LA - eng

KW - reflexive Banach space; Schauder basis; quotient space; w$^*$-basic sequence; tensor product; reflexive Banach space; Schauder basis; quotient space; w-basic sequence; tensor product

UR - http://eudml.org/doc/30977

ER -

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