On EP elements, normal elements and partial isometries in rings with involution
نویسندگان
چکیده
This is a continuation to the study of EP elements, normal elements and partial isometries in rings with involution. The aim of this paper is to give the negative solution to three conjectures on this subject. Moreover, some new characterizations of EP elements in rings with involution are presented.
منابع مشابه
Ela on Ep Elements, Normal Elements and Partial Isometries in Rings with Involution
This is a continuation to the study of EP elements, normal elements and partial isometries in rings with involution. The aim of this paper is to give the negative solution to three conjectures on this subject. Moreover, some new characterizations of EP elements in rings with involution are presented.
متن کاملFurther results on partial isometries and EP elements in rings with involution
We investigate elements in rings with involution which are EP or partial isometries. Some well-known results are generalized.
متن کاملPartial isometries and EP elements in rings with involution
If R is a ring with involution, and a† is the Moore-Penrose inverse of a ∈ R, then the element a is called: EP, if aa† = a†a; partial isometry, if a∗ = a†; star-dagger, if a∗a† = a†a∗. In this paper, characterizations of partial isometries, EP elements and star-dagger elements in rings with involution are given. Thus, some well-known results are extended to more general settings.
متن کاملNew characterizations of EP, generalized normal and generalized Hermitian elements in rings
We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy ana∗ = a∗an or a = (a∗)n for arbitrary n ∈ N . For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution.
متن کاملPartial Isometries and EP Elements in Banach Algebras
and Applied Analysis 3 The left multiplication by a ∈ A is the mapping La : A → A, which is defined as La x ax for all x ∈ A. Observe that, for a, b ∈ A, Lab LaLb and that La Lb implies a b. If a ∈ A is both Moore-Penrose and group invertible, then La† La † and La# La # in the Banach algebraL A . According to 4, Remark 12 , a necessary and sufficient condition for a ∈ A to be EP is that La ∈ L ...
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تاریخ انتشار 2017