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A product of three projections

Eva Kopecká, Vladimír Müller (2014)

Studia Mathematica

Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam Paszkiewicz...

A projective central limit theorem and interacting Fock space representation for the limit process

Vitonofrio Crismale (2007)

Banach Center Publications

Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.

A proof of the Grünbaum conjecture

Bruce L. Chalmers, Grzegorz Lewicki (2010)

Studia Mathematica

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define λ ₙ N = s u p λ ( V ) : d i m ( V ) = n , V ⊂ l ∞ ( N ) , λₙ = supλ(V): dim(V) = n. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Grünbaum conjecture is presented

A properly infinite Banach *-algebra with a non-zero, bounded trace

H. G. Dales, Niels Jakob Laustsen, Charles J. Read (2003)

Studia Mathematica

A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.

A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let C c ( G ) be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that ( C c ( G ) , ε G ) has property (FH) if and only if G has property (T). On...

A property of ergodic flows

Maria Joiţa, Radu-B. Munteanu (2014)

Studia Mathematica

We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III₀ whose associated flow has this property is not of product type. A consequence is that a properly ergodic flow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which-up to conjugacy-is built under a function with the dyadic odometer as base automorphism.

Currently displaying 681 – 700 of 1578