Point-spectrum of semibounded operator extensions

One-point extensions of locally compact paracompact spaces

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

A Floquet Operator with Pure Point Spectrum and Energy Instability

It is not immediate whether a self-adjoint operator H with purely point spectrum implies absence of transport under the time evolution U(t) = e−iHt; in fact, it is currently known examples of Schrödinger operators with such kind of spectrum and transport. In case of tight-binding models on l2(IN) the transport is usually probed by the moments of order m > 0 of the position operator Xek = kek, t...

Operator Extensions of Hua’s Inequality

Abstract. We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is eq...

Operator Extensions on Hilbert Space

Triplet Extensions I: Semibounded Operators in the Scale of Hilbert Spaces

The extension theory for semibounded symmetric operators is generalized by including operators acting in a triplet of Hilbert spaces. We concentrate our attention on the case where the minimal operator is essentially self-adjoint in the basic Hilbert space and construct a family of its self-adjoint extensions inside the triplet. All such extensions can be described by certain boundary condition...