共查询到20条相似文献,搜索用时 626 毫秒
1.
Piotr Niemiec 《Integral Equations and Operator Theory》2011,71(2):151-160
Generalized absolute values as well as corresponding to them generalized polar decompositions of a bounded linear operator
T of a Hilbert space H{\mathcal{H}} into a Hilbert space K{\mathcal{K}} are defined, motivated by the inequality |áTx, y?K|2 £ á|T|x, x?Há|T*|y, y?K{|\langle{Tx}, {y}\rangle}_{\mathcal{K}}|^2 \leq \langle|T|x, {x}\rangle_{\mathcal{H}}\langle{|T^{*}|y}, {y}\rangle_{\mathcal{K}} . It is shown that there is a natural bijection between generalized absolute values of T and of T* which sends |T| to |T*|. For a bounded nonnegative operator A on H{\mathcal{H}} and a bounded Borel function
f: \mathbbR+ ? \mathbbR+{f: \mathbb{R}_+ \to \mathbb{R}_+} , equivalent conditions for A and f(|T|) to be generalized absolute values of T are established and corresponding to them generalized absolute values of T* are determined. 相似文献
2.
I. P. Il’inskaya 《Ukrainian Mathematical Journal》2009,61(7):1113-1122
We study the arithmetic of a semigroup MP\mathcal{M}_{\mathcal{P}} of functions with operation of multiplication representable in the form f(x) = ?n = 0¥ ancn(x) ( an 3 0,?n = 0¥ an = 1 ) f(x) = \sum\nolimits_{n = 0}^\infty {{a_n}{\chi_n}(x)\quad \left( {{a_n} \ge 0,\sum\nolimits_{n = 0}^\infty {{a_n} = 1} } \right)} , where { cn }n = 0¥ \left\{ {{\chi_n}} \right\}_{n = 0}^\infty is a system of multiplicative functions that are generalizations of the classical Walsh functions. For the semigroup MP\mathcal{M}_{\mathcal{P}}, analogs of the well-known Khinchin theorems related to the arithmetic of a semigroup of probability measures in R
n
are true. We describe the class I0(MP)I_0(\mathcal{M}_{\mathcal{P}}) of functions without indivisible or nondegenerate idempotent divisors and construct a class of indecomposable functions that
is dense in MP\mathcal{M}_{\mathcal{P}} in the topology of uniform convergence. 相似文献
3.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
{ x ? X|t - q\textRea y1 ( tA )x, t - q\textRea y2 ( tA )x ? L*p ( ( 0,¥ );X ) } {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} 相似文献
4.
We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set $\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}
5.
Approximation to the function |x| plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals |x| if α = 1. We construct a Newman Type Operator rn(x) and prove max |x|≤1|xαsgn x-rn(x)|~Cn1/4e-π1/2(1/2)αn. 相似文献
6.
Let
C( \mathbbRm ) C\left( {{\mathbb{R}^m}} \right) be the space of bounded and continuous functions
x:\mathbbRm ? \mathbbR x:{\mathbb{R}^m} \to \mathbb{R} equipped with the norm
|