ORCID Profile
0000-0003-2275-8579
Current Organisation
The University of Edinburgh
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Publisher: Element d.o.o.
Date: 2012
DOI: 10.7153/OAM-06-20
Publisher: Elsevier
Date: 1988
Publisher: Informa UK Limited
Date: 10-04-2021
Publisher: Elsevier BV
Date: 03-2001
Publisher: MDPI AG
Date: 13-01-2020
Abstract: The longstanding Banach–Mazur separable quotient problem asks whether every infinite-dimensional Banach space has a quotient (Banach) space that is both infinite-dimensional and separable. Although it remains open in general, an affirmative answer is known in many special cases, including (1) reflexive Banach spaces, (2) weakly compactly generated (WCG) spaces, and (3) Banach spaces which are dual spaces. Obviously (1) is a special case of both (2) and (3), but neither (2) nor (3) is a special case of the other. A more general result proved here includes all three of these cases. More precisely, we call an infinite-dimensional Banach space X dual-like, if there is another Banach space E, a continuous linear operator T from the dual space E * onto a dense subspace of X, such that the closure of the kernel of T (in the relative weak* topology) has infinite codimension in E * . It is shown that every dual-like Banach space has an infinite-dimensional separable quotient.
Publisher: Elsevier BV
Date: 06-2019
Publisher: Springer Science and Business Media LLC
Date: 22-11-2019
Publisher: Wiley
Date: 12-1988
Publisher: Det Kgl. Bibliotek/Royal Danish Library
Date: 06-1982
Publisher: Det Kgl. Bibliotek/Royal Danish Library
Date: 12-2001
DOI: 10.7146/MATH.SCAND.A-14339
Abstract: If $\\mathcal P$, $\\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\\mathcal P$-by-$\\mathcal Q$ (or is a $\\mathcal P$-by-$\\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\\mathcal P$ such that the corresponding quotient $X/Y$ has property $\\mathcal Q$. The choices $\\mathcal P,\\mathcal Q \\in\\{\\hbox{separable, reflexive}\\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For ex le, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new ex le of a Banach space property which is not a 3-space property but whose dual is a 3-space property.
Publisher: Wiley
Date: 06-1979
Publisher: Elsevier BV
Date: 11-2006
Publisher: Springer Berlin Heidelberg
Date: 1983
DOI: 10.1007/BFB0061578
Publisher: Michigan Mathematical Journal
Date: 1989
Publisher: Elsevier BV
Date: 06-2002
Publisher: Cambridge University Press (CUP)
Date: 1984
DOI: 10.1017/S0017089500005395
Abstract: Let E be an ordered Banach space with closed positive cone C . A base for C is a convex subset K of C with the property that every non-zero element of C has a unique representation of the form λ k with λ 0 and k ∈ K . Let S be the absolutely convex hull of K . If the Minkowski functional of S coincides with the given norm on E , then E is called a base norm space. Then K is a closed face of the unit ball of E , and S contains the open unit ball of E . Base norm spaces were first defined by Ellis [5, p. 731], although the special case of dual Banach spaces had been studied earlier by Edwards [4].
Publisher: Elsevier
Date: 2004
Publisher: Springer Science and Business Media LLC
Date: 04-1988
DOI: 10.1007/BF01190235
Publisher: Centre pour la Communication Scientifique Directe (CCSD)
Date: 22-04-2020
DOI: 10.46298/DMTCS.6369
Abstract: this is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide ex les of maximizers, for any d.
Publisher: Elsevier BV
Date: 2019
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 21-11-2022
DOI: 10.1137/21M144832X
Publisher: Springer Science and Business Media LLC
Date: 19-04-2019
Publisher: Springer International Publishing
Date: 2020
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 1988
Publisher: Cambridge University Press (CUP)
Date: 02-1989
DOI: 10.1017/S0013091500006908
Abstract: Given any subspace N of a Banach space X , there is a subspace M containing N and of the same density character as N , for which there exists a linear Hahn–Banach extension operator from M * to X *. This result was first proved by Heinrich and Mankiewicz [ 4 , Proposition 3.4] using some of the deeper results of Model Theory. More precisely, they used the Banach space version of the Löwenheim–Skolem theorem due to Stern [ 11 ], which in turn relies on the Löwenheim–Skolem and Keisler–Shelah theorems from Model Theory. Previously Lindenstrauss [ 7 ], using a finite dimensional lemma and a compactness argument, obtained a version of this for reflexive spaces. We shall show that the same finite dimensional lemma leads directly to the general result, without any appeal to Model Theory.
Publisher: Cambridge University Press (CUP)
Date: 12-1982
DOI: 10.1017/S0004972700005827
Abstract: We give a simple proof of the fact that compact, connected topological spaces have the “average distance property”. For a metric space ( X, d ), this asserts the existence of a unique number a = a ( X ) such that, given finitely many points x 1 , …, x n ∈ X , then there is some y ∈ X with We examine the possible values of a ( X ) , for subsets of finite dimensional normed spaces. For ex le, if diam( X ) denotes the diameter of some compact, convex set in a euclidean space, then a ( X ) ≤ diam( X )/√2 . On the other hand, a ( X )/diam( X ) can be arbitrarily close to 1 , for non-convex sets in euclidean spaces of sufficiently large dimension.
Publisher: Cambridge University Press (CUP)
Date: 04-1979
DOI: 10.1017/S0004972700010972
Abstract: Let E be a Banach space, M a closed subspace of E with the 3-ball property. It is known that M is proximinal in E , and that its metric projection admits a continuous selection. This means that there is a continuous (generally non-linear) map π: E → M satisfying ‖ x −π( x )‖ = d ( x , M ) for all x in E . Here it is shown that the same conclusion holds under a much weaker hypothesis on M , which we call the 1½-ball property. We also establish that if M has the 1½-ball property in E , then there is a continuous Hahn-Banach extension map from M * to E *.
Publisher: The Electronic Journal of Combinatorics
Date: 15-07-2022
DOI: 10.37236/10374
Abstract: We define two $d$-polytopes, both with $2d+2$ vertices and $(d+3)(d-1)$ edges, which reduce to the cube and the 5-wedge in dimension three. We show that they are the only minimisers of the number of edges, amongst all $d$-polytopes with $2d+2$ vertices, when $d=6$ or $d\\ge8$. We also characterise the minimising polytopes for $d=4, 5$ or 7, where four sporadic ex les arise.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2018
DOI: 10.1137/17M1131994
Publisher: American Mathematical Society (AMS)
Date: 02-07-2003
DOI: 10.1090/S0002-9947-03-03152-0
Abstract: If X X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 → C ( K ) → Y → X → 0 0\\to C(K)\\to Y\\to X\\to 0 , where K = [ 0 , 1 ] K=[0,1] or ω ω . \\omega ^{\\omega }. For the case K = [ 0 , 1 ] K=[0,1] we show that there exists a twisted sum whose quotient map is strictly singular if and only if X X contains no copy of ℓ 1 \\ell _1 . If K = ω ω K=\\omega ^{\\omega } we prove an analogue of a theorem of Johnson and Zippin (for K = [ 0 , 1 ] K=[0,1] ) by showing that all such twisted sums are trivial if X X is the dual of a space with summable Szlenk index (e.g., X X could be Tsirelson’s space) a converse is established under the assumption that X X has an unconditional finite-dimensional decomposition. We also give conditions for the existence of a twisted sum with C ( ω ω ) C(\\omega ^{\\omega }) with strictly singular quotient map.
Publisher: Cambridge University Press (CUP)
Date: 10-1986
DOI: 10.1017/S1446788700033607
Abstract: The notion of quasi-regularity, defined for optimization problems in R n , is extended to the Banach space setting. Ex les are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.
Publisher: Springer Science and Business Media LLC
Date: 19-12-2020
Publisher: Springer Science and Business Media LLC
Date: 03-2008
Publisher: JSTOR
Date: 04-1986
DOI: 10.2307/2323675
Publisher: Springer International Publishing
Date: 2018
Publisher: Springer International Publishing
Date: 2018
Publisher: Canadian Mathematical Society
Date: 21-05-2018
DOI: 10.4153/S0008414X18000123
Abstract: We study $n$ -vertex $d$ -dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes . We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$ , and $s$ , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$ . We characterize the minimizers and provide ex les of maximizers for any $d$ . Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.
Publisher: JSTOR
Date: 02-1981
DOI: 10.2307/2044212
Publisher: Informa UK Limited
Date: 10-2007
Publisher: Institute of Mathematics, Polish Academy of Sciences
Date: 1988
Publisher: Elsevier BV
Date: 02-1987
Publisher: Michigan Mathematical Journal
Date: 1995
Publisher: Cambridge University Press (CUP)
Date: 06-1984
DOI: 10.1017/S0013091500022318
Abstract: Recall that a norm and monotone if and monotone if If the norm is both absolute and monotone, itis called a Riesz norm. It is easy to show that a norm is Riesz if and only if whenever A Banach lattice is a vector lattice equipped with a complete Riesznorm.
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for David Yost.