Small eigenvalue variation and real rank zero
نویسندگان
چکیده
منابع مشابه
Separative Exchange Rings and C * - Algebras with Real Rank Zero
For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ∼= A ⊕ B ∼= B ⊕ B =⇒ A ∼= B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(R) is surjective. In combination with a result of Huaxin Lin, it follow...
متن کاملInvertibility-preserving Maps of C∗-algebras with Real Rank Zero
In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...
متن کاملEigenvalue computation for unitary rank structured matrices
In this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps. First we perform a reduction of the given matrix into Hessenberg form, next we compute the eigenvalues of this resulting Hessenberg matrix via an implicit QR-algorithm. Along the way, we explainhow the knowledge of a certain ‘shift’ correction term to the structure can be used to speed up ...
متن کاملOn the Classification of Simple Z-stable C-algebras with Real Rank Zero and Finite Decomposition Rank
We show that, if A is a separable simple unital C-algebra which absorbs the Jiang–Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C-algebras as above which, additionally, satisfy the Universal Coeff...
متن کاملZero forcing parameters and minimum rank problems
Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by 2 G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive 3 semidefinite zero forcing number Z+(G) is introduced, and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1996
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1996.175.47