Book ChapterDOI
On the Lipschitz Decomposition Problem in Ordered Banach Spaces and Its Connections to Other Branches of Mathematics
Miek Messerschmidt
- pp 405-423
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TLDR
For any Banach space X, ordered by a closed generating cone C ⊆ X, do there always exist Lipschitz functions ⋅+ : X → C and ⋆− : x → C satisfying x = x+ − x− for every x ∈ X?Abstract:
Consider the following still-open problem: for any Banach space X, ordered by a closed generating cone C ⊆ X, do there always exist Lipschitz functions ⋅+ : X → C and ⋅− : X → C satisfying x = x+ − x− for every x ∈ X?read more
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Banach Lattices and Positive Operators
TL;DR: In this paper, the authors propose the use of linear operators on positive matrices and apply it to non-positive matrices, including the case of positive projections. But they do not consider the case where positive projections are defined by a linear operator.
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TL;DR: Godefroy as discussed by the authors provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts, and encourages graduate students interested in learning more about Banach spaces.
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Introduction to Tensor Products of Banach Spaces
TL;DR: In this article, a self-contained introduction to the theory of tensor products of Banach spaces is provided for graduate students in analysis or for researchers in other fields who wish to become acquainted with this area The only prerequisite are a basic knowledge of functional analysis and measure theory.
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Tensor Norms and Operator Ideals
Andreas Defant,Klaus Floret +1 more
TL;DR: Tensor Norms and Operator Ideals as mentioned in this paper are a generalization of the algebraic theory of Tensor Products and have been studied extensively in the literature, e.g. in the context of algebraic theories of tensors.