On generalized eigenfunctions of operators in a Hilbert space
We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.
An operator T acting on a Banach space X has property (gw) if , where is the approximate point spectrum of T, is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and .
A two-sided sequence with values in a complex unital Banach algebra is a cosine sequence if it satisfies for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence is bounded if . A (bounded) group decomposition for a cosine sequence is a representation of c as for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...
A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.
A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.