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We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.

On a theorem of Lebow

W. Mlak (1977)

Annales Polonici Mathematici

On a theorem of Lebow and Mlak for several commuting operators

J. Janas (1983)

Studia Mathematica

On an integral of fractional power operators

Nick Dungey (2009)

Colloquium Mathematicae

For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator $V ̃ = \int_{0}^{\infty} d α V^{α}$ . We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum 0, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.

On bare and semibare points for some classes of operators

Istratescu, V., Istratescu, I. (1970)

Portugaliae mathematica

On certain quantities in Fredholm operator theory and Mil'man's isometry spectrum

Beucher, O. J. (1985)

Proceedings of the 13th Winter School on Abstract Analysis

On complex interpolation and spectral continuity

Karen Saxe (1998)

Studia Mathematica

Let ${[X_{0}, X_{1}]}_{t}$ , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both $X_{0}$ and $X_{1}$ will act boundedly on each ${[X_{0}, X_{1}]}_{t}$ . Let $T_{t}$ denote such an operator when considered on ${[X_{0}, X_{1}]}_{t}$ , and $σ (T_{t})$ denote its spectrum. We are motivated by the question of whether or not the map $t \to σ (T_{t})$ is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: $t \to {(σ (T_{t}))}^{\land}$ (polynomially convex hull) and $t \to \partial_{e} (σ (T_{t}))$ (boundary of the polynomially convex...

On continuity of linear transformations commuting with generalized scalar operators (Preliminary communication)

Pavla Gvozdková (1970)

Commentationes Mathematicae Universitatis Carolinae

On coupling constant thresholds and related eigenvalue properties of Dirac operators.

M. Klaus (1985)

Journal für die reine und angewandte Mathematik

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