To do this, we need to study thequotient algebra B(H)/K(H) (called the Calkin algebra), as well as the notion ofFredholm operator and essential spectrum of an operator. These notions are alsowidely used to study problems in global analysis and PDE. Throughout, H will be a Hilbert ...
(2009), The essential spectrum of an operator arising in 2-dimensional magneto-hydrodynamics. Math. Nachr., 282: 422–429. doi: 10.1002/mana.200810745 Author Information 1 School of Mathematics and Statistics, The University of New South Wales, UNSW Sydney, NSW 2052, Australia 2 NWF I – ...
Spectrum of a Model Operator in the Pertur- bation Theory of the Essential Spectrum. Theor. Math. Phys. 144, No. 3, 1344-1352 (2005).G. R. Yodgorov and M. E´ . Muminov, Spectrum of a Model Operator in the Perturba- tion Theory of the Essential Spectrum, Theor. Math. Phys. ...
For an operator 𝑇, acting between Hilbert spaces, it is shown that and are respectively the maximal and the minimal elements of the essential spectrum of , and that 𝑇 is AMD-regular if and only if the essential spectrum of |𝑇| consists of a single point. Key words and phrases::...
On the invariance of the essential spectrum of an arbitrary operator. III We provide sufficient conditions under which the difference of the resolventsof two higher-order operators acting in $\\R^N$ belongs to trace classes$\\cC^... Schechter,Martin - 《Mathematical Proceedings of the Cambridge...
Essential selfadjointness and invariance of the essential spectrum for Dirac operators 3JL Let T be a densely defined closable linear operator in a Hilbert space X and Let Q(x) be anHermitian symmetric matrix-valued measurable function satisfying one of the following The proofunder the assumption...
On the essential spectrum of the Laplacian on complete manifolds The author proves two theorems on when the essential spectrum of the Laplace-Beltrami operator on a complete manifold M satisfying a generalized "pole condition" is equal to an interval [c,∞). The condition on M is that it con...
On Essential Selfadjointness, Distinguished Selfadjoint Extension and Essential Spectrum of Dirac Operators with Matrix Valued Potentials 来自 Semantic Scholar 喜欢 0 阅读量: 5 作者: M Arai 摘要: (1.2) ajak+akaj=2djkl (/, fe = l, 2, 3, 4). We denote by HQ the operator H with We ...
Abstract Volterra operatoressential spectrummeasure of noncompactnessIt is shown that for abstract linear Volterra operators the spectral radius is the essential spectral radius. The result is applied to prove the existence of a global solution of a Volterra-Hammerstein functional inclusion when the ...
Recently,some excellent achievements in researches of the joint spectrum and thejoint essential spectrum of n-tuple operators have been attained.In this paper,basedon the new achievements mentioned above,the author will discuss the joint Browderessential spectrum of n-tuple operators first defined by ...