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Linear Spaces And Approximation by Paul Leo Butzer

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1Banach Spaces Of Linear Operators And Homogeneous Polynomials Without The Approximation Property

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We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13].

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The book is available for download in "texts" format, the size of the file-s is: 0.11 Mbs, the file-s for this book were downloaded 45 times, the file-s went public at Fri Jun 29 2018.

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2Restricted Non-linear Approximation In Sequence Spaces And Applications To Wavelet Bases And Interpolation

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Restricted non-linear approximation is a type of N-term approximation where a measure $\nu$ on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper and lower Temlyakov property. As applications we obtain results for wavelet bases in Triebel-Lizorkin spaces by showing the Temlyakow property in this setting. Moreover, new interpolation results for Triebel-Lizorkin and Besov spaces are obtained.

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  • Title: ➤  Restricted Non-linear Approximation In Sequence Spaces And Applications To Wavelet Bases And Interpolation
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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: 11.68 Mbs, the file-s for this book were downloaded 157 times, the file-s went public at Sat Sep 21 2013.

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3Approximation Properties Of Locally Convex Spaces And The Problem Of Uniqueness Of The Trace Of A Linear Operator

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In the present article, it is proved that every nuclear operator in a locally convex space E has a well-defi?ned trace if E possesses the approximation property. However, even if a space possesses the approximation property this still does not guarantee a positive solution of A. Grothendieck's uniqueness problem for this space. Below, we present an example of a quasi-complete space with the approximation property in which it is not possible to de?fine the trace for all Fredholm operators (in the sense of A. Grothendieck). We prove that the uniqueness problem has a positive solution if E possesses the "bounded approximation property." Preliminary information and results are presented in Section 2. A number of approximation-type properties of locally convex spaces and relations between these properties are considered in Section 3. The principal results of the present study, along with certain corollaries from these results (for example, the existence of a matrix trace), may be found in Section 4.

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The book is available for download in "texts" format, the size of the file-s is: 9.22 Mbs, the file-s for this book were downloaded 78 times, the file-s went public at Sat Sep 21 2013.

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