Displaying similar documents to “A note on the differentiable structure of generalized idempotents”

Metrics in the sphere of a C*-module

Esteban Andruchow, Alejandro Varela (2007)

Open Mathematics

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Given a unital C*-algebra 𝒜 and a right C*-module 𝒳 over 𝒜 , we consider the problem of finding short smooth curves in the sphere 𝒮 𝒳 = x ∈ 𝒳 : 〈x, x〉 = 1. Curves in 𝒮 𝒳 are measured considering the Finsler metric which consists of the norm of 𝒳 at each tangent space of 𝒮 𝒳 . The initial value problem is solved, for the case when 𝒜 is a von Neumann algebra and 𝒳 is selfdual: for any element x 0 ∈ 𝒮 𝒳 and any tangent vector ν at x 0, there exists a curve γ(t) = e tZ(x 0), Z ∈ ℒ 𝒜 ( 𝒳 ) , Z* = −Z and...

Boundedness properties of resolvents and semigroups of operators

J. van Casteren (1997)

Banach Center Publications

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Let T: H → H be an operator in the complex Hilbert space H. Suppose that T is square bounded in average in the sense that there exists a constant M(T) with the property that, for all natural numbers n and for all x ∈ H, the inequality 1 / ( n + 1 ) ∑ j = 0 n ∥ T j x ∥ 2 ≤ M ( T ) 2 ∥ x ∥ 2 is satisfied. Also suppose that the adjoint T* of the operator T is square bounded in average with constant M(T*). Then the operator T is power bounded in the sense that s u p ∥ T i n ∥ : n ∈ ℕ is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*)....

Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar (2014)

Open Mathematics

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For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

Integral representations of unbounded operators by infinitely smooth kernels

Igor Novitskiî (2005)

Open Mathematics

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In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.

Fragmented deformations of primitive multiple curves

Jean-Marc Drézet (2013)

Open Mathematics

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A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also...