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1.
Let
be a unital C*-algebra and G the group of units of
. A geometrical study of the action of G over the set
+ of all positive elements of
is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure. 相似文献
2.
Jorge Antezana Gustavo Corach Demetrio Stojanoff 《Integral Equations and Operator Theory》2006,55(2):169-188
If
$$\mathcal{H}$$ is a Hilbert space,
$$\mathcal{S}$$ is a closed subspace of
$$\mathcal{H},$$ and A is a positive bounded linear operator on
$$\mathcal{H},$$ the spectral shorted operator
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence
$$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes
$$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to
$$\mathcal{S}.$$ We characterize the left spectral resolution of
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ and show several properties of this operator, particularly in the case that
dim
$${\mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional
case and for non invertible operators. 相似文献
3.
J. Antezana G. Corach M. Ruiz D. Stojanoff 《Proceedings of the American Mathematical Society》2006,134(4):1031-1037
We characterize those frames on a Hilbert space which can be represented as the image of an orthonormal basis by an oblique projection defined on an extension of . We show that all frames with infinite excess and frame bounds are of this type. This gives a generalization of a result of Han and Larson which only holds for normalized tight frames.
4.
5.
A partial isometry V is said to be a split partial isometry if ${\mathcal{H}=R(V) + N(V)}$ , with R(V) ∩ N(V) = {0} (R(V) = range of V, N(V) = null-space of V). We study the topological properties of the set ${\mathcal{I}_0}$ of such partial isometries. Denote by ${\mathcal{I}}$ the set of all partial isometries of ${\mathcal{B}(\mathcal{H})}$ , and by ${\mathcal{I}_N}$ the set of normal partial isometries. Then $$\mathcal{I}_N\subset \mathcal{I}_0\subset \mathcal{I}, $$ and the inclusions are proper. It is known that ${\mathcal{I}}$ is a C ∞-submanifold of ${\mathcal{B}(\mathcal{H})}$ . It is shown here that ${\mathcal{I}_0}$ is open in ${\mathcal{I}}$ , therefore is has also C ∞-local structure. We characterize the set ${\mathcal{I}_0}$ , in terms of metric properties, existence of special pseudo-inverses, and a property of the spectrum and the resolvent of V. The connected components of ${\mathcal{I}_0}$ are characterized: ${V_0,V_1\in \mathcal{I}_0}$ lie in the same connected component if and only if $${\rm dim}\, R(V_0)= {\rm dim}\, R(V_1) \,\,{\rm and}\,\,\, {\rm dim}\, R(V_0)^\perp = {\rm dim}\, R(V_1)^\perp.$$ This result is known for normal partial isometries. 相似文献
6.
Gustavo Corach Alejandra Maestripieri 《Numerical Functional Analysis & Optimization》2013,34(6):659-673
A generalization with singular weights of Moore–Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators. 相似文献
7.
Several new notions of stable ranks for commutative Banach algebras are introduced. Due to the fact that they depend on certain orthogonal groups, they are called real stable ranks and are finer than their complex counterparts. 相似文献
8.
9.
Gustavo Corach Alejandra Maestripieri Demetrio Stojanoff 《Proceedings of the American Mathematical Society》2006,134(3):765-778
If is a Hilbert space, is a positive bounded linear operator on and is a closed subspace of , the relative position between and establishes a notion of compatibility. We show that the compatibility of is equivalent to the existence of a convenient orthogonal projection in the operator range with its canonical Hilbertian structure.
10.
Research supported by CONICET, Argentina 相似文献