排序方式: 共有18条查询结果,搜索用时 15 毫秒
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Bojan Magajna 《Transactions of the American Mathematical Society》1996,348(6):2427-2440
Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.
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Bojan Magajna 《Integral Equations and Operator Theory》2016,85(1):37-62
We prove a geometric version of an operator valued Hahn–Banach theorem and use it to study sets K that are A-convex over a unital C*-algebra A in the sense that \({\sum_{j=1}^{n} a_{j}^{*}y_{j}a_{j}\in K}\) whenever \({y_{j}\in K}\) and \({a_{j}\in A}\) with \({\sum_{j=1}^{n}a_{j}^{*}a_{j}=1}\). We show how weak* compact such sets can be realized as concrete sets of unital completely positive maps. An application to C*-extreme points is also presented. 相似文献
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Bojan Magajna 《Complex Analysis and Operator Theory》2018,12(8):1903-1927
We investigate boundary representations in the context where Hilbert spaces are replaced by \(\hbox {C}^{*}\)-modules over abelian von Neumann algebras and apply this to study \(\hbox {C}^{*}\)-extreme points. We present an (unexpected) example of a weak* compact \(\mathcal {B}\)-convex subset of \({\mathbb {B}}(\mathcal {H})\) without \(\mathcal {B}\)-extreme points, where \(\mathcal {B}\) is an abelian von Neumann algebra on a Hilbert space \(\mathcal {H}\). On the other hand, if \(\mathcal {A}\) is a von Neumann algebra with a separable predual and whose finite part is injective, we show that each weak* compact \(\mathcal {A}\)-convex subset of \(\ell ^{\infty }(\mathcal {A})\) is generated by its \(\mathcal {A}\)-extreme points. 相似文献
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Bojan Magajna 《Proceedings of the American Mathematical Society》2004,132(6):1747-1754
The norm of the operator on (or on any prime C-algebra ) is computed for all and is shown to be equal to the completely bounded norm.
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We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak*-continuous on dual spaces. In particular, if X is a subspace of a C*-algebra A, and if a∈A satisfies aX⊂X, then we show that the function x?ax on X is automatically weak* continuous if either (a) X is a dual operator space, or (b) a*X⊂X and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C*-subalgebra. Applications include a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W*-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra. 相似文献
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Bojan Magajna 《Journal of Mathematical Analysis and Applications》2009,350(1):252-255
We prove that if a unital Banach algebra A is the dual of a Banach space A? then the set of normal states is weak∗ dense in the set of all states on A. Further, normal states linearly span A?. 相似文献
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Bojan Magajna 《Proceedings of the American Mathematical Society》2001,129(3):771-780
Each weak* compact C-convex set in a hyperfinite factor (in particular in ) is the weak* closure of the C-convex hull of its C-extreme points.
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Bojan Magajna 《Journal of Functional Analysis》2005,219(2):306-339
For an operator bimodule X over von Neumann algebras A⊆B(H) and B⊆B(K), the space of all completely bounded A,B-bimodule maps from X into B(K,H), is the bimodule dual of X. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To X a normal operator bimodule Xn is associated so that completely bounded A,B-bimodule maps from X into normal operator bimodules factorize uniquely through Xn. A construction of Xn in terms of biduals of X, A and B is presented. Various operator bimodule structures are considered on a Banach bimodule admitting a normal such structure. 相似文献
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A finite simplicial complex is orderable if its simplices are the chains of a poset. For each closed surface an orderable triangulation is given that is minimal with respect to the number of vertices. The construction of minimal ordered triangulations implies that for each surface S the minimal number of vertices of a bipartite graph, which has a quadrilateral embedding into S, is equal to b(S) = ?4 + (16 – 8χ)1/2?, where χ is the Euler characteristic of S. 相似文献