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Banach Spaces Of Continuous Functions. by Zbigniew Semadeni

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1Schauder Bases In Banach Spaces Of Continuous Functions

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  • Title: ➤  Schauder Bases In Banach Spaces Of Continuous Functions
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 316.32 Mbs, the file-s for this book were downloaded 16 times, the file-s went public at Thu Aug 11 2022.

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2Banach Spaces Of Continuous Functions

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  • Title: ➤  Banach Spaces Of Continuous Functions
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 1664.31 Mbs, the file-s for this book were downloaded 19 times, the file-s went public at Thu Aug 25 2022.

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3On Isomorphisms Of Banach Spaces Of Continuous Functions

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We prove that if $K$ and $L$ are compact spaces and $C(K)$ and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base consisting of open sets $U$ such that $\bar{U}$ is a continuous image of some compact subspace of $L$. This gives some information on isomorphic classes of the spaces of the form $C([0,1]^\kappa)$ and $C(K)$ where $K$ is Corson compact.

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  • Title: ➤  On Isomorphisms Of Banach Spaces Of Continuous Functions
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 7.44 Mbs, the file-s for this book were downloaded 52 times, the file-s went public at Sun Sep 22 2013.

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4Operators On Two Banach Spaces Of Continuous Functions On Locally Compact Spaces Of Ordinals

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Denote by $[0,\omega_1)$ the set of countable ordinals, equipped with the order topology, let $L_0$ be the disjoint union of the compact ordinal intervals $[0,\alpha]$ for $\alpha$ countable, and consider the Banach spaces $C_0[0,\omega_1)$ and $C_0(L_0)$ consisting of all scalar-valued, continuous functions which are defined on the locally compact Hausdorff spaces $[0,\omega_1)$ and $L_0$, respectively, and which vanish eventually. Our main result states that a bounded operator $T$ between any pair of these two Banach spaces fixes a copy of $C_0(L_0)$ if and only if the identity operator on $C_0(L_0)$ factors through $T$, if and only if the Szlenk index of $T$ is uncountable. This implies that the set $\mathscr{S}_{C_0(L_0)}(C_0(L_0))$ of $C_0(L_0)$-strictly singular operators on $C_0(L_0)$ is the unique maximal ideal of the Banach algebra $\mathscr{B}(C_0(L_0))$ of all bounded operators on $C_0(L_0)$, and that $\mathscr{S}_{C_0(L_0)}(C_0[0,\omega_1))$ is the second-largest proper ideal of $\mathscr{B}(C_0[0,\omega_1))$. Moreover, it follows that the Banach space $C_0(L_0)$ is primary and complementably homogeneous.

“Operators On Two Banach Spaces Of Continuous Functions On Locally Compact Spaces Of Ordinals” Metadata:

  • Title: ➤  Operators On Two Banach Spaces Of Continuous Functions On Locally Compact Spaces Of Ordinals
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 5.49 Mbs, the file-s for this book were downloaded 106 times, the file-s went public at Sat Jul 20 2013.

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5Quotients Of Continuous Convex Functions On Nonreflexive Banach Spaces

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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.

“Quotients Of Continuous Convex Functions On Nonreflexive Banach Spaces” Metadata:

  • Title: ➤  Quotients Of Continuous Convex Functions On Nonreflexive Banach Spaces
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 3.06 Mbs, the file-s for this book were downloaded 83 times, the file-s went public at Sat Sep 21 2013.

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