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Math: Each bounded linear operator on Hilbert space has invariant subspace

“In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier ...
JSTOR Daily

Invariant Subspaces for Bounded Operators with Large Localizable Spectrum

Suppose H is a complex Hilbert space and T ∈ L(H) is a bounded operator. For each closed set F $\subset$ C let HT(F) denote the corresponding spectral manifold. Let σloc(T) denote the set of all ...
Scientific Research Publishing

Nemytskii Operator in the Space of Set-Valued Functions of Bounded φ-Variation ()

This research was partly supported by CDCHTA of Universidad de Los Andes under the project NURR-C- 547-12-05-B. Conflicts of Interest The authors declare no conflicts of interest. [1] A. Smajdor and W ...
JSTOR Daily

Nonzero Fixed Points of Power-Bounded Linear Operators

Proceedings of the American Mathematical Society, Vol. 131, No. 5 (May, 2003), pp. 1539-1551 (13 pages) This paper provides a variety of sufficient conditions for the existence of a nonzero fixed ...
Scientific Research Publishing

On Eigenvalues and Boundary Curvature of the Numerical Rang of Composition Operators on Hardy Space ()

1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran. For a bounded linear operator A on a Hilbert space, the numerical range is the image of the unit sphere of under the ...
IEEE

A Note on an elementary Operator with Quasi-M-Hyponormal Operator Entries

Abstract: A bounded operator T on the Hilbert space H is called quasi-M-hyponormal if there exists a positive real number M such that $T^{*}\left(M^{2}(T-\lambda ...