اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدReverse Cholesky factorization and tensor products of nest algebras
53
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that every positive semidefinite matrix over the natural numbers that is eventually 0 in each row and column can be factored as the product of an upper triangular matrix times a lower triangular matrix. We also extend some known results about factorization with respect to tensor products of nest algebras. Our proofs use the theory of reproducing kernel Hilbert spaces.
قيم البحث
اقرأ أيضاً
We show that the tensor product of two cyclic $A_infty$-algebras is, in general, not a cyclic $A_infty$-algebra, but an $A_infty$-algebra with homotopy inner product. More precisely, we construct an explicit combinatorial diagonal on the pairahedra,
which are contractible polytopes controlling the combinatorial structure of an $A_infty$-algebra with homotopy inner products, and use it to define a categorically closed tensor product. A cyclic $A_infty$-algebra can be thought of as an $A_infty$-algebra with homotopy inner products whose higher inner products are trivial. However, the higher inner products on the tensor product of cyclic $A_infty$-algebras are not necessarily trivial.
Given two complex Banach spaces $X_1$ and $X_2$, a tensor product of $X_1$ and $X_2$, $X_1tilde{otimes}X_2$, in the sense of J. Eschmeier ([5]), and two finite tuples of commuting operators, $S=(S_1,ldots ,S_n)$ and $T=(T_1,ldots ,T_m)$, defined on $
X_1$ and $X_2$ respectively, we consider the $(n+m)$-tuple of operators defined on $X_1tilde{otimes}X_2$, $(Sotimes I,Iotimes T)= (S_1otimes I,ldots ,S_notimes I,Iotimes T_1,ldots ,I otimes T_m)$, and we give a description of the semi-Browder joint spectra introduced by V. Kordula, V. Muller and V. Rako$check{c}$evi$acute{ c}$ in [7] and of the split semi-Browder joint spectra (see section 3), of the $(n+m)$-tuple $(Sotimes I ,Iotimes T)$, in terms of the corresponding joint spectra of $S$ and $T$. This result is in some sense a generalization of a formula obtained for other various Browder spectra in Hilbert spaces and for tensor products of operators and for tuples of the form $(Sotimes I ,Iotimes T)$. In addition, we also describe all the mentioned joint spectra for a tuple of left and right multiplications defined on an operator ideal between Banach spaces in the sense of [5].
We study ring-theoretic (in)finiteness properties -- such as emph{Dedekind-finiteness} and emph{proper infiniteness} -- of ultraproducts (and more generally, reduced products) of Banach algebras. Whilst we characterise when an ultraproduct has thes
e ring-theoretic properties in terms of its underlying sequence of algebras, we find that, contrary to the $C^*$-algebraic setting, it is not true in general that an ultraproduct has a ring-theoretic finiteness property if and only if ultrafilter many of the underlying sequence of algebras have the same property. This might appear to violate the continuous model theoretic counterpart of {L}oss Theorem; the reason it does not is that for a general Banach algebra, the ring theoretic properties we consider cannot be verified by considering a bounded subset of the algebra of emph{fixed} bound. For Banach algebras, we construct counter-examples to show, for example, that each component Banach algebra can fail to be Dedekind-finite while the ultraproduct is Dedekind-finite, and we explain why such a counter-example is not possible for $C^*$-algebras. Finally the related notion of having textit{stable rank one} is also studied for ultraproducts.
The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner algebra of
Y. Furthermore, this subalgebra can be described in a natural way in terms of the gauge actions on the Cuntz-Pimsner algebras. We explore implications for graph algebras, crossed products by the integers, and crossed products by completely positive maps. We also give a new proof of a result of Kaliszewski and Quigg related to coactions on correspondences.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
