Spectrum of a particular bounded self-adjoint linear operator
نویسندگان
چکیده
منابع مشابه
Decomposition of the spectrum of a bounded linear operator
1σ(T ) is defined to be the set of λ ∈ C such that v 7→ Tv − λv is not a bijection. It is a fact that if T ∈ B(H) and v 7→ Tv − λv is a bijection then it is an element of B(H). That it is linear can be proved quickly. The fact that it is bounded is proved using the open-mapping theorem, which states that a surjective bounded linear map from one Banach space to another is an open map, from which...
متن کاملRegularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation
In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.
متن کاملThe Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum
Pauli’s well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamiltonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate t...
متن کاملAn Unusual Self-adjoint Linear Partial Differential Operator
In an American Mathematical Society Memoir, to appear in 2003, the authors Everitt and Markus apply their prior theory of symplectic algebra to the study of symmetric linear partial differential expressions, and the generation of self-adjoint differential operators in Sobolev Hilbert spaces. In the case when the differential expression has smooth coefficients on the closure of a bounded open re...
متن کاملIndex theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations
We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making use of the dual variational methods and Morse theory. Finally, some interesting examples concerning second order Hamiltonian systems, first order Hamiltonian ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2001
ISSN: 1370-1444
DOI: 10.36045/bbms/1102714037