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Search: All articles in the CMB digital archive with keyword spectrum

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1. CMB 2012 (vol 57 pp. 37)

Dashti, Mahshid; Nasr-Isfahani, Rasoul; Renani, Sima Soltani
Character Amenability of Lipschitz Algebras
Let ${\mathcal X}$ be a locally compact metric space and let ${\mathcal A}$ be any of the Lipschitz algebras ${\operatorname{Lip}_{\alpha}{\mathcal X}}$, ${\operatorname{lip}_{\alpha}{\mathcal X}}$ or ${\operatorname{lip}_{\alpha}^0{\mathcal X}}$. In this paper, we show, as a consequence of rather more general results on Banach algebras, that ${\mathcal A}$ is $C$-character amenable if and only if ${\mathcal X}$ is uniformly discrete.

Keywords:character amenable, character contractible, Lipschitz algebras, spectrum
Categories:43A07, 46H05, 46J10

2. CMB 2012 (vol 57 pp. 145)

Mustafayev, H. S.
The Essential Spectrum of the Essentially Isometric Operator
Let $T$ be a contraction on a complex, separable, infinite dimensional Hilbert space and let $\sigma \left( T\right) $ (resp. $\sigma _{e}\left( T\right) )$ be its spectrum (resp. essential spectrum). We assume that $T$ is an essentially isometric operator, that is $I_{H}-T^{\ast }T$ is compact. We show that if $D\diagdown \sigma \left( T\right) \neq \emptyset ,$ then for every $f$ from the disc-algebra, \begin{equation*} \sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma _{e}\left( T\right) \right) , \end{equation*} where $D$ is the open unit disc. In addition, if $T$ lies in the class $ C_{0\cdot }\cup C_{\cdot 0},$ then \begin{equation*} \sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma \left( T\right) \cap \Gamma \right) , \end{equation*} where $\Gamma $ is the unit circle. Some related problems are also discussed.

Keywords:Hilbert space, contraction, essentially isometric operator, (essential) spectrum, functional calculus
Categories:47A10, 47A53, 47A60, 47B07

3. CMB 2009 (vol 52 pp. 66)

Dryden, Emily B.; Strohmaier, Alexander
Huber's Theorem for Hyperbolic Orbisurfaces
We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.

Keywords:Huber's theorem, length spectrum, isospectral, orbisurfaces
Categories:58J53, 11F72

4. CMB 2000 (vol 43 pp. 51)

Edward, Julian
Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
The growth properties at infinity for eigenfunctions corresponding to embedded eigenvalues of the Neumann Laplacian on horn-like domains are studied. For domains that pinch at polynomial rate, it is shown that the eigenfunctions vanish at infinity faster than the reciprocal of any polynomial. For a class of domains that pinch at an exponential rate, weaker, $L^2$ bounds are proven. A corollary is that eigenvalues can accumulate only at zero or infinity.

Keywords:Neumann Laplacian, horn-like domain, spectrum
Categories:35P25, 58G25

5. CMB 1998 (vol 41 pp. 196)

Nakazi, Takahiko
Brown-Halmos type theorems of weighted Toeplitz operators
The spectra of the Toeplitz operators on the weighted Hardy space $H^2(Wd\th/2\pi)$ and the Hardy space $H^p(d\th/2\pi)$, and the singular integral operators on the Lebesgue space $L^2(d\th/2\pi)$ are studied. For example, the theorems of Brown-Halmos type and Hartman-Wintner type are studied.

Keywords:Toeplitz operator, singular integral, operator, weighted Hardy space, spectrum.
Category:47B35

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