Search results for "commutator"

P4730Underweight is associated with unfavourable short- and long-term outcomes after MitraClip therapy: a body mass index derived subgroup analysis o…

2019

Abstract Background Underweight and obesity represent classical risk factors for patients undergoing cardiac surgery or interventional treatment. The multicentre German Transcatheter Mitral Valve Interventions (TRAMI) registry comprises a large and prospectively enrolled real-world cohort of patients treated by MitraClip implantation. Aims The current analysis examines the impact of underweight, overweight and obesity on intra-hospital, short and long-term outcomes in patients treated by MitraClip therapy. Methods and results From 08/2010 until 07/2013, 799 patients (age 75.3±8.6 years, male gender 60.7%, median logistic EuroSCORE 20% [12; 31], functional mitral regurgitation (MR): 69.3%) w…

On the spectrum of linear combinations of two projections inC*-algebras

2010

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.

Extension of a Schur theorem to groups with a central factor with a bounded section rank

2013

Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.

Structure of Kac-Moody groups

2008

For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,

Commutators of linear and bilinear Hilbert transforms

2003

Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ⁡ ( α 1 ) = sign ⁡ ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…

Commutator anomalies and the Fock bundle

1990

We show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic Fock spaces parametrized by vector potentials, and more generally, by splittings of the fermionic one-particle space into a pair of complementary subspaces. On the Lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies.

The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras

2018

The notion of the equationally-defined commutator was introduced and thoroughly investigated in (Czelakowski, 2015). In this work the properties of the equationally-defined commutator in quasivarieties generated by two-element algebras are examined. It is proved: If a quasivariety Q is generated by a finite set of two-element algebras, then the equationally-defined commutator of Q is additive (Theorem 3.1) Moreover it satisfies the associativity law (Theorem 3.6). The second result is strengthened if the quasivariety is generated by a single two-element algebra 2: If Q = SP(2), then the equationally-defined commutator of Q universally validates one of the following laws: [x,y] = x^y or [x,y…

Commutator Laws in Finitely Generated Quasivarieties

2015

Weak commutation relations of unbounded operators and applications

2011

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.

Verbal sets and cyclic coverings

2010

Abstract We consider groups G such that the set of all values of a fixed word w in G is covered by a finite set of cyclic subgroups. Fernandez-Alcober and Shumyatsky studied such groups in the case when w is the word [ x 1 , x 2 ] , and proved that in this case the corresponding verbal subgroup G ′ is either cyclic or finite. Answering a question asked by them, we show that this is far from being the general rule. However, we prove a weaker form of their result in the case when w is either a lower commutator word or a non-commutator word, showing that in the given hypothesis the verbal subgroup w ( G ) must be finite-by-cyclic. Even this weaker conclusion is not universally valid: it fails …