A proof of the Russo-Dye theorem for -algebras.
Siddiqui, Akhlaq A. (2010)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Martingale convergence theorems in -algebras.”
A proof of the Russo-Dye theorem for -algebras.
Convex combinations of unitaries in -algebras.
Siddiqui, Akhlaq A. (2011)
The New York Journal of Mathematics [electronic only]
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Chain rules for canonical state extensions on von Neumann algebras
Carlo Cecchini, Dénes Petz (1993)
Colloquium Mathematicae
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In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von...
Log-majorizations and norm inequalities for exponential operators
Fumio Hiai (1997)
Banach Center Publications
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Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means. ...
The closure of the invertibles in a von Neumann algebra
Laura Burlando, Robin Harte (1996)
Colloquium Mathematicae
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In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results,...
The -function in -algebras.
Siddiqui, Akhlaq A. (2011)
The New York Journal of Mathematics [electronic only]
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Simple finite Jordan pseudoalgebras.
Kolesnikov, Pavel (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Nonassociative normed algebras: geometric aspects
Angel Rodríguez Palacios (1994)
Banach Center Publications
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Introduction. The aim of this paper is to review some relevant results concerning the geometry of nonassociative normed algebras, without assuming in the first instance that such algebras satisfy any familiar identity, like associativity, commutativity, or Jordan axiom. In the opinion of the author, the most impressive fact in this direction is that most of the celebrated natural geometric conditions that can be required for associative normed algebras, when imposed on...
On some von Neumann topological algebras.
Choukri, Rachid, El Kinani, Abdellah, Oudadess, Mohamed (2009)
Banach Journal of Mathematical Analysis [electronic only]
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On unitary convex decompositions of vectors in a -algebra
Akhlaq A. Siddiqui (2013)
Archivum Mathematicum
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By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital -algebra permits the vector decomposable as convex combination of fewer unitaries; certain -algebra results due to M. Rørdam have been extended to the general setting of -algebras.