Displaying similar documents to “Positive projections as generators of J -projections of type (B).”

A metric on the space of projections admitting nice isometries

Lajos Molnár, Werner Timmermann (2009)

Studia Mathematica

Similarity:

Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical...

Topology of the isometry group of the Urysohn space

Julien Melleray (2010)

Fundamenta Mathematicae

Similarity:

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise,...

A product of three projections

Eva Kopecká, Vladimír Müller (2014)

Studia Mathematica

Similarity:

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...

Metric abstract elementary classes with perturbations

Åsa Hirvonen, Tapani Hyttinen (2012)

Fundamenta Mathematicae

Similarity:

We define an abstract setting suitable for investigating perturbations of metric structures generalizing the notion of a metric abstract elementary class. We show how perturbation of Hilbert spaces with an automorphism and atomic Nakano spaces with bounded exponent fit into this framework, where the perturbations are built into the definition of the class being investigated. Further, assuming homogeneity and some other properties true in the example classes, we develop a notion of independence...

Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time

V. Khatskevich, L. Zelenko (2006)

Studia Mathematica

Similarity:

We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible...