Displaying similar documents to “Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems”

The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Paweł Głowacki (1998)

Studia Mathematica

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Let A be a pseudodifferential operator on ℝ N whose Weyl symbol a is a strictly positive smooth function on W = ℝ N × ℝ N such that | ∂ α a | ≤ C α a 1 - ϱ for some ϱ>0 and all |α|>0, ∂ α a is bounded for large |α|, and l i m w → ∞ a ( w ) = ∞ . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin. ...

Pointwise multiplication operators on weighted Banach spaces of analytic functions

J. Bonet, P. Domański, M. Lindström (1999)

Studia Mathematica

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For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator M φ , M φ ( f ) = φ f , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when M φ ' is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M φ ' .

A resolvent condition implying power boundedness

Béla Nagy, Jaroslav Zemánek (1999)

Studia Mathematica

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The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.

Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

A. Böttcher, M. Seybold (2000)

Studia Mathematica

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The discrete Wiener-Hopf operator generated by a function a ( e i θ ) with the Fourier series ∑ n ∈ ℤ a n e i n θ is the operator T(a) induced by the Toeplitz matrix ( a j - k ) j , k = 0 ∞ on some weighted sequence space l p ( ℤ + , w ) . We assume that w satisfies the Muckenhoupt A p condition and that a is a piecewise continuous function subject to some natural multiplier condition. The last condition is in particular satisfied if a is of bounded variation. Our main result is a Fredholm criterion and an index formula for T(a). It implies that the...

Inequalities for exponentials in Banach algebras

A. Pryde (1991)

Studia Mathematica

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For commuting elements x, y of a unital Banach algebra ℬ it is clear that ∥ e x + y ∥ ≤ ∥ e x ∥ ∥ e y ∥ . On the order hand, M. Taylor has shown that this inequality remains valid for a self-adjoint operator x and a skew-adjoint operator y, without the assumption that they commute. In this paper we obtain similar inequalities under conditions that lie between these extremes. The inequalities are used to deduce growth estimates of the form ∥ e ' ∥ ≤ c ( 1 + | ξ | ⟩ s for all ξ ∈ R m , where x = ( x 1 , . . . , x m ) ∈ ℬ m and c, s are constants.

Some spectral inequalities involving generalized scalar operators

B. Aupetit, D. Drissi (1994)

Studia Mathematica

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In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu,...