The Type I Part of the Regular Representation

1974 ◽  
Vol 26 (5) ◽  
pp. 1086-1089 ◽  
Author(s):  
Edward Formanek
Keyword(s):  
Discrete Group ◽  
Regular Representation ◽  
Complex Numbers ◽  
Type I ◽  
Bounded Operators ◽  
Weak Operator Topology ◽  
Weak Operator ◽  
Image Position ◽  
The Right

Let G be a discrete group and let H = L2(G), with norm | |. Let B(H) be the ring of bounded operators on H with the normThe right regular representation of G on H induces an injection ρ : C[G] → B(H), and W(G) is the closure of the image of ρ in the weak operator topology on B(H) (C = complex numbers). Using ρ, we identify C[G] with its image in W(G).

Polynomial Invariant Theory and Taylor Series

1991 ◽  
Vol 43 (6) ◽  
pp. 1243-1262 ◽  
Author(s):  
John E. Gilbert
Keyword(s):  
Irreducible Representation ◽  
Taylor Series ◽  
Invariant Theory ◽  
Regular Representation ◽  
Polynomial Functions ◽  
Polynomial Invariant ◽  
Finite Dimensional ◽  
Isotypic Component ◽  
Image Position ◽  
The Right

For any group K and finite-dimensional (right) K-module V let be the right regular representation of K on the algebra of polynomial functions on V. An Isotypic Component of is the sum of all k-submodules of on which π restricts to an irreducible representation can then be written as f = ΣƬ ƒƬ with ƒƬ in .

scholarly journals C*-Algebras of inverse semigroups

1985 ◽  
Vol 28 (1) ◽  
pp. 41-58 ◽  
Author(s):  
J. Duncan ◽  
A. L. T. Paterson
Keyword(s):  
Banach Algebra ◽  
Group Ring ◽  
Discrete Group ◽  
Regular Representation ◽  
Inverse Semigroups ◽  
C Algebras ◽  
Complex Group ◽  
Left Regular Representation ◽  
Left Regular ◽  
Image Position

There are various algebras which may be associated with a discrete group G. In particular we may consider the complex group ring ℂG, the convolution Banach algebra l1(G), the enveloping C*-algebra C*(G) of l1(G), and the reduced C*-algebra determined by the completion of l1(G) under the left regular representation on l2(G). There is a substantial literature on the circle of ideas associated with the embeddings

Weakly Compact, Operator-Valued Derivations of Type I Von Neumann Algebras

1984 ◽  
Vol 36 (3) ◽  
pp. 436-457
Author(s):  
Steve Wright
Keyword(s):  
Von Neumann Algebras ◽  
Linear Operators ◽  
Type I ◽  
Weakly Compact ◽  
Bounded Linear ◽  
Von Neumann ◽  
Weakly Compact Operator ◽  
Weak Operator ◽  
Image Position ◽  
Compact Extension

In [18], the author initiated an investigation of compact, Banach-module-valued derivations of C*-algebras. In collaboration with C. A. Akemann [3] and S.-K. Tsui [16], he determined the structure of all compact and weakly compact, A-valued derivations of a C*-algebra A, and of all compact, B(H)-valued derivations of a C*-subalgebra of B(H), the algebra of bounded linear operators on a Hilbert space H. In this paper, we begin the study of weakly compact, B(H)-valued derivations of C*-subalgebras of B(H).Let R be a C*-subalgebra of B(H), δ:R → B(H) a weakly compact derivation, i.e., a weakly compact linear map which hasSince δ has a unique weakly compact extension to a derivation of the closure of R in the weak operator topology (WOT) on B(H) (consult the proof of Theorem 3.1 of [16]), we may assume with no loss of generality that R is a von Neumann subalgebra of B(H). In this paper, we determine in Lemma 4.1 and Theorems 4.3 and 4.10 the structure of δ when R is type I, using I. E. Segal's multiplicity theory [14] for type I von Neumann algebras and results of E. Christensen [6], [7] on B(H)-valued derivations of von Neumann algebras.

On the almost sure approximation of self-adjoint operators in L2 (0, 1)

1996 ◽  
Vol 119 (3) ◽  
pp. 537-543
Author(s):  
L. J. Ciach ◽  
R. Jajte ◽  
A. Paszkiewicz
Keyword(s):  
Adjoint Operator ◽  
Almost Sure Convergence ◽  
The Other ◽  
Orthogonal Projections ◽  
Weak Operator Topology ◽  
Weak Operator ◽  
Image Position ◽  
Adjoint Operators ◽  
Orthogonal Systems ◽  
Martingale Convergence

There are several important theorems concerning the almost sure convergence of (monotone) sequences of orthogonal projections in L2-spaces. Let us mention here the martingale convergence theorems or the results on the developments of functions with respect to orthogonal systems. On the other hand every self-adjoint operator with the spectrum on the interval [0, 1] is a limit of some sequence of orthogonal projections in the weak operator topology (see [1]). This paper is devoted to a problem of approximation of a self-adjoint operator A acting in L2 (0, 1) by a sequence Pn of orthogonal projections in the sense that

scholarly journals Elementary operators on prime C*-algebras II

1988 ◽  
Vol 30 (3) ◽  
pp. 275-284 ◽  
Author(s):  
Martin Mathieu
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Regular Representation ◽  
Bounded Operators ◽  
Weakly Compact ◽  
C Algebras ◽  
Left Regular Representation ◽  
Left Regular ◽  
Elementary Operators ◽  
The Right

Compact elementary operators acting on the algebra ℒ(H) of all bounded operators on some Hilbert space H were characterised by Fong and Sourour in [9]. Akemann and Wright investigated compact and weakly compact derivations on C*-algebras [1], and also studied compactness properties of the sum and the product of the right and the left regular representation of an element in a C*-algebra [2]. They used the concept of a compact Banach algebra element due to Vala [17]: an element a in a Banach algebra A is called compact if the mapping x → axa is compact on A. This notion has been further investigated by Ylinen [18, 19, 20], who showed in particular that a is a compact element of the C*-algebra A if x ↦ axa is weakly compact on A [19].

On the Ranges of Certain Fractional Integrals

1972 ◽  
Vol 24 (6) ◽  
pp. 1198-1216 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Banach Space ◽  
Fractional Integrals ◽  
Complex Numbers ◽  
Bounded Operators ◽  
Image Position

Suppose 1 ≦ P < ∞, μ is real, and denote by Lμ,p the collection of functions f, measurable on (0, ∞ ), and which satisfy1.1Also denote by [X] the collection of bounded operators from a Banach space X to itself. For v > 0, Re α > 0, Re β > 0, let1.2and1.3where ξ and η are complex numbers. Iv,α,ξ and Jv,β,η, are generalizations of the Riemann-Liouville and Weyl fractional integrals respectively, and consequently we shall refer to them as fractional integrals.

Residual Gas Reactions in the Electron Microscope: I. Qualitative Observations on the Water Gas Reaction

1968 ◽  
Vol 26 ◽  
pp. 292-293
Author(s):  
Richard E. Hartman ◽  
Roberta S. Hartman ◽  
Peter L. Ramos
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Gas Phase ◽  
Absolute Temperature ◽  
Residual Gas ◽  
Gas Reactions ◽  
Image Position ◽  
The Right ◽  
Water Gas ◽  
Thinning Rate

The action of water and the electron beam on organic specimens in the electron microscope results in the removal of oxidizable material (primarily hydrogen and carbon) by reactions similar to the water gas reaction .which has the form:The energy required to force the reaction to the right is supplied by the interaction of the electron beam with the specimen.The mass of water striking the specimen is given by:where u = gH2O/cm2 sec, PH2O = partial pressure of water in Torr, & T = absolute temperature of the gas phase. If it is assumed that mass is removed from the specimen by a reaction approximated by (1) and that the specimen is uniformly thinned by the reaction, then the thinning rate in A/ min iswhere x = thickness of the specimen in A, t = time in minutes, & E = efficiency (the fraction of the water striking the specimen which reacts with it).

Right Ventricle Mass Removal from Tricuspid Valve Apparatus: An Unusual Thromboembolic Complication of Severe Ketoacidosis

2016 ◽  
Vol 19 (2) ◽  
pp. 077
Author(s):  
Ireneusz Haponiuk ◽  
Maciej Chojnicki ◽  
Konrad Paczkowski ◽  
Wojciech Kosiak ◽  
Radosław Jaworski ◽  
...  
Keyword(s):  
Right Ventricle ◽  
Tricuspid Valve ◽  
Mild Hypothermia ◽  
Heart Function ◽  
Thromboembolic Complication ◽  
Surgical Removal ◽  
Unusual Complication ◽  
Type I ◽  
Definitive Therapy ◽  
The Right

The presence of a pathologic mass in the right ventricle (RV) may lead to hemodynamic consequences and to a life-threatening incident of pulmonary embolism. The diagnosis of an unstable thrombus in the right heart chamber usually necessitates intensive treatment to dissolve or remove the pathology. We present a report of an unusual complication of severe ketoacidosis: thrombus in the right ventricle, removed from the tricuspid valve (TV) apparatus. A four-year-old boy was diagnosed with diabetes mellitus (DM) type I de novo. During hospitalization, a 13.9 × 8.4 mm tumor in the RV was found in a routine cardiac ultrasound. The patient was referred for surgical removal of the floating lesion from the RV. The procedure was performed via midline sternotomy with extracorporeal circulation (ECC) and mild hypothermia. Control echocardiography showed complete tumor excision with normal atrioventricular valves and heart function. Surgical removal of the thrombus from the tricuspid valve apparatus was effective, safe, and a definitive therapy for thromboembolic complication of pediatric severe ketoacidosis.<br /><br />

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

scholarly journals Relaxing cosmological neutrino mass bounds with unstable neutrinos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Miguel Escudero ◽  
Jacobo Lopez-Pavon ◽  
Nuria Rius ◽  
Stefan Sandner
Keyword(s):  
Neutrino Mass ◽  
Particle Physics ◽  
Goldstone Boson ◽  
Mass Scale ◽  
Simple Extension ◽  
Type I ◽  
Mass Generation ◽  
Age Of The Universe ◽  
Neutrino Mass Models ◽  
The Right

Abstract At present, cosmological observations set the most stringent bound on the neutrino mass scale. Within the standard cosmological model (ΛCDM), the Planck collaboration reports ∑mv< 0.12 eV at 95 % CL. This bound, taken at face value, excludes many neutrino mass models. However, unstable neutrinos, with lifetimes shorter than the age of the universe τν ≲ tU, represent a particle physics avenue to relax this constraint. Motivated by this fact, we present a taxonomy of neutrino decay modes, categorizing them in terms of particle content and final decay products. Taking into account the relevant phenomenological bounds, our analysis shows that 2-body decaying neutrinos into BSM particles are a promising option to relax cosmological neutrino mass bounds. We then build a simple extension of the type I seesaw scenario by adding one sterile state ν4 and a Goldstone boson ϕ, in which νi→ ν4ϕ decays can loosen the neutrino mass bounds up to ∑mv ∼ 1 eV, without spoiling the light neutrino mass generation mechanism. Remarkably, this is possible for a large range of the right-handed neutrino masses, from the electroweak up to the GUT scale. We successfully implement this idea in the context of minimal neutrino mass models based on a U(1)μ−τ flavor symmetry, which are otherwise in tension with the current bound on ∑mv.

Sign in / Sign up

Export Citation Format

Share Document