Displaying similar documents to “Invariance properties of the Laplace operator”

On m -sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry

Ognjen Milatovic (2004)

Commentationes Mathematicae Universitatis Carolinae

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We consider a Schrödinger-type differential expression H V = ∇ * ∇ + V , where ∇ is a C ∞ -bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry ( M , g ) with metric g and positive C ∞ -bounded measure d μ , and V is a locally integrable section of the bundle of endomorphisms of E . We give a sufficient condition for m -sectoriality of a realization of H V in L 2 ( E ) . In the proof we use generalized Kato’s inequality as well as a result on the positivity of u ∈ L 2 ( M ) satisfying...

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if f ( σ W ( T ) ) ∪ z ∈ ℂ : | z | = 1 is connected, where σ W ( T ) denotes the Weyl spectrum of T.

Non-commutative Gelfand-Naimark theorem

Janusz Migda (1993)

Commentationes Mathematicae Universitatis Carolinae

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We show that if Y is the Hausdorffization of the primitive spectrum of a C * -algebra A then A is * -isomorphic to the C * -algebra of sections vanishing at infinity of the canonical C * -bundle over Y .