1,792 research outputs found
On non-adjointable semi-Weyl and semi-B-Fredholm operators over C*-algebras
We extend further semi-A-Fredholm theory by generalizing the results from
classical semi-Weyl theory on Hilbert spaces. Moreover, we obtain an analogue
of the results from [17] in the setting of non-adjointable operators. Finally,
we provide several examples on semi-A-Fredholm and semi- A-Weyl operators over
a unital C*-algebra A. We give also the examples of semi-A-Fredholm operators
with non-closed image
On excesses of frames
We show that any two frames in a separable Hilbert space that are dual to
each other have the same excess. Some new relations for the analysis resp.
synthesis operators of dual frames are also derived. We then prove that
pseudo-dual frames and, in particular, approximately dual frames have the same
excess. We also discuss various results on frames in which excesses of frames
play an important role.Comment: 12 page
Deformations of quantum field theories on spacetimes with Killing vector fields
The recent construction and analysis of deformations of quantum field
theories by warped convolutions is extended to a class of curved spacetimes.
These spacetimes carry a family of wedge-like regions which share the essential
causal properties of the Poincare transforms of the Rindler wedge in Minkowski
space. In the setting of deformed quantum field theories, they play the role of
typical localization regions of quantum fields and observables. As a concrete
example of such a procedure, the deformation of the free Dirac field is
studied.Comment: 35 pages, 3 figure
The Birman-Schwinger principle in von Neumann algebras of finite type
We introduce a relative index for a pair of dissipative operators in a von
Neumann algebra of finite type and prove an analog of the Birman-Schwinger
principle in this setting. As an application of this result, revisiting the
Birman-Krein formula in the abstract scattering theory, we represent the de la
Harpe-Skandalis determinant of the characteristic function of dissipative
operators in the algebra in terms of the relative index
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