共查询到20条相似文献,搜索用时 156 毫秒
1.
This paper resolves a number of problems in the perturbation theory of linear operators, linked with the 45-year-old conjecure
of M. G. Kreĭn. In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals
S
α
, 1 < α < ∞. Alternatively, for every 1 < α < ∞, there is a constant c
α
> 0 such that
|| f(a) - f(b) ||a \leqslant ca|| f ||\textLip 1|| a - b ||a, {\left\| {f(a) - f(b)} \right\|_{\alpha }} \leqslant {c_{\alpha }}{\left\| f \right\|_{{{\text{Lip}}\,{1}}}}{\left\| {a - b} \right\|_{\alpha }}, 相似文献
2.
S. P. Eveson 《Integral Equations and Operator Theory》2005,53(3):331-341
Given k ∈ L1 (0,1) satisfying certain smoothness and growth conditions at 0, we consider the Volterra convolution operator Vk defined on Lp (0,1) by
3.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,34(1):91-106
For an operatorT satisfying thatT
*(T
*
T–TT
*)T0, we shall show that and, moreover, tr
itT isn-multicyclic.For an operatorT satisfying thatT
*
{(T
*
T)
p
–(TT
*)
p
}T0 for somep (0, 1], we shall show that
and, moreover,
ifT isn-multicyclic. 相似文献
4.
On the Isolated Points of the Spectrum of Paranormal Operators 总被引:1,自引:0,他引:1
Atsushi Uchiyama 《Integral Equations and Operator Theory》2006,55(1):145-151
For paranormal operator T on a separable complex Hilbert space
we show that (1) Weyl’s theorem holds for T, i.e., σ(T) \ w(T) = π00(T) and (2) every Riesz idempotent E with respect to a non-zero isolated point λ of σ(T) is self-adjoint (i.e., it is an orthogonal projection) and satisfies that ranE = ker(T − λ) = ker(T − λ)*. 相似文献
5.
The paper [2] defines the noncoinciding irreducibility sets N
2(a, σ) and N
3(a, σ), σ ∈ (0, 2a], of all n-dimensional linear differential systems with piecewise continuous coefficient matrices A(t) such that ‖A(t)‖ ≤ a < + ∞ for t ∈ [0,+∞) and there exists a linear differential system that is not Lyapunov reducible to the original system and has coefficient
matrix B(t) satisfying [for the case of N
2(a, σ)] the condition
|