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1
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On the Normality of the Unbounded Product of Two Normal Operators

100%
Mortad M. H.
Concrete Operators
|
2013
|
tom 1
11-18
EN
Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
2
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A new view of some operators and their properties in terms of the Non-Newtonian Calculus

100%
Ünlüyol E., Salas S., Iscan I.
Topological Algebra and its Applications
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2017
|
tom 5
|
nr 1
49-54
EN
Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of substraction and addition into division and multiplication, respectively and thus established a new calculus, called Non-Newtonian Calculus. So in this paper, it is investigated to a new view of some operators and their properties in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.
3
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A note on the differentiable structure of generalized idempotents

100%
Andruchow E., Corach G., Mbekhta M.
Open Mathematics
|
2013
|
tom 11
|
nr 6
1004-1019
EN
For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.
4
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General numerical radius inequalities for matrices of operators

76%
Al-Dolat M., Al-Zoubi K., Ali M., Bani-Ahmad F.
Open Mathematics
|
2016
|
tom 14
|
nr 1
109-117
EN
Let Ai ∈ B(H), (i = 1, 2, ..., n), and [...] T=[ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.
5
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The algebraic size of the family of injective operators

64%
Bernal-González L.
Open Mathematics
|
2017
|
tom 15
|
nr 1
13-20
EN
In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.
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