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LSpice
LSpice
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Does the second Bourgain DelbaenBourgain–Delbaen space belong to C_p?

The second Bourgain-DelbaenBourgain–Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$. The dual space is isomorphic to $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurmnorm null ones.

A Banach space $X\in C_p$ if the identity map i$i$ on X$X$ is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

Does the second Bourgain Delbaen space belong to C_p

The second Bourgain-Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$. The dual space is isomorphic to $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurm null ones.

A Banach space $X\in C_p$ if the identity map i on X is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

Does the second Bourgain–Delbaen space belong to C_p?

The second Bourgain–Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$. The dual space is isomorphic to $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to norm null ones.

A Banach space $X\in C_p$ if the identity map $i$ on $X$ is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

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Ioana Ghenciu
Ioana Ghenciu
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The second Bourgain-Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$. The dual space is isomorphic to $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurm null ones.

A Banach space $X\in C_p$ if the identity map i on X is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

The second Bourgain-Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurm null ones.

A Banach space $X\in C_p$ if the identity map i on X is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

The second Bourgain-Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$. The dual space is isomorphic to $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurm null ones.

A Banach space $X\in C_p$ if the identity map i on X is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?

Source Link
Ioana Ghenciu
Ioana Ghenciu
  • 81
  • 2

Does the second Bourgain Delbaen space belong to C_p

The second Bourgain-Delbaen space $Y$ is a separable $\mathcal{L}_\infty$ space such that $Y$ contains no copy of $c_0$ or $\ell_1$.

An operator $T:X\to Y$ is $p$-convergent if it takes weakly $p$-summable sequences to nurm null ones.

A Banach space $X\in C_p$ if the identity map i on X is $p$-convergent.

It is known that $X\in C_p$ if and only if every operator $T:\ell_{p^*}\to X$ is compact, where $p^*$ is the conjugate of $p$.

Is $Y\in C_p$ for some $1<p<\infty$ ? Is $Y\in C_2$?