Mappings preserving approximate orthogonality in Hilbert $C^*$-modules
نویسندگان
چکیده
منابع مشابه
Orthogonality preserving mappings on inner product C* -modules
Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...
متن کاملLinear Orthogonality Preservers of Hilbert C∗-modules
We show in this paper that the module structure and the orthogonality structure of a Hilbert C∗-module determine its inner product structure. Let A be a C∗-algebra, and E and F be Hilbert A-modules. Assume Φ : E → F is an A-module map satisfying 〈Φ(x),Φ(y)〉A = 0 whenever 〈x, y〉A = 0. Then Φ is automatically bounded. In case Φ is bijective, E is isomorphic to F . More precisely, let JE be the cl...
متن کاملApproximate isometries in Hilbert C ∗ - modules ∗
We use the fixed point alternative theorem to prove that, under suitable conditions, every A-valued approximate isometry on a Hilbert C∗-module over the C∗-algebra A can be approximated by a unique A-valued isometry. AMS subject classifications: Primary 39B52, 39B82, 46B04, 46L08; Secondary 47H10
متن کاملOn Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras
We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.
متن کاملApproximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules
In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames 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: MATHEMATICA SCANDINAVICA
سال: 2018
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-102945