Square Root Closed C∗-algebras
نویسندگان
چکیده
We say that a C∗-algebra A is approximately square root closed, if any normal element in A can be approximated by a square of a normal element in A. We study when A is approximately square root closed, and have an affirmative answer for AI-algebras, Goodearl type algebras over the torus, purely infinite simple unital C∗-algebras etc.
منابع مشابه
ON COMMUTATIVE AND NON-COMMUTATIVE C-ALGEBRAS WITH THE APPROXIMATE n-TH ROOT PROPERTY
We say that a C∗-algebra X has the approximate n-th root property (n ≥ 2) if for every a ∈ X with ‖a‖ ≤ 1 and every ε > 0 there exits b ∈ X such that ‖b‖ ≤ 1 and ‖a − bn‖ < ε. Some properties of commutative and non-commutative C∗-algebras having the approximate nth root property are investigated. In particular, it is shown that there exists a non-commutative (resp., commutative) separable unita...
متن کاملPrimitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...
متن کاملar X iv : m at h / 05 09 00 6 v 1 [ m at h . FA ] 1 S ep 2 00 5 ROOT CLOSED FUNCTION ALGEBRAS ON COMPACTA OF LARGE DIMENSION
Let X be a Hausdorff compact space and C(X) be the algebra of all continuous complex-valued functions on X, endowed with the supremum norm. We say that C(X) is (approximately) n-th root closed if any function from C(X) is (approximately) equal to the n-th power of another function. We characterize the approximate n-th root closedness of C(X) in terms of ndivisibility of first Čech cohomology gr...
متن کاملP-CLOSURE IN PSEUDO BCI-ALGEBRAS
In this paper, for any non-empty subset C of a pseudo BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is introduced and some related properties are investigated. Applying this concept, a characterization of the minimal elements of X is given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X containing C and K(X) for any ideal C of X...
متن کاملDerivations on dual triangular Banach algebras
Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007