The Drazin Inverses of Infinite Triangular Matrices and Their Linear Preservers

Słowik, Roksana

doi:10.1007/s11253-018-1520-1

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2021

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“…Lemma 1 (Słowik (2018), Lemma 2.1) Suppose F is a field of characteristic different from 2. If x ∈ T ∞ (F) is tripotent, then there exists an invertible t ∈ T ∞ (F) such that x t is a diagonal matrix.…”

Section: First Resultsmentioning

confidence: 99%

Jordan triple homomorphisms on $${\mathcal {T}}_\infty (F)$$

Słowik

2021

Beitr Algebra Geom

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Let $${\mathcal {T}}_\infty (F)$$ T ∞ ( F ) be the algebra of all $${\mathbb {N}}\times {\mathbb {N}}$$ N × N upper triangular matrices defined over a field F of characteristic different from 2. We consider the Jordan triple homomorphisms of $${\mathcal {T}}_\infty (F)$$ T ∞ ( F ) , i.e. the additive maps that satisfy the condition $$\phi (xyx)=\phi (x)\phi (y)\phi (x)$$ ϕ ( x y x ) = ϕ ( x ) ϕ ( y ) ϕ ( x ) for all $$x,y\in {\mathcal {T}}_\infty (F)$$ x , y ∈ T ∞ ( F ) . For the case when F is a prime field we find the form of all such maps $$\phi $$ ϕ . For the general case we present the form of the surjective maps $$\phi $$ ϕ .

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Section: First Resultsmentioning

confidence: 99%

Jordan triple homomorphisms on $${\mathcal {T}}_\infty (F)$$

Słowik

2021

Beitr Algebra Geom

View full text Add to dashboard Cite

show abstract

The Drazin Inverses of Infinite Triangular Matrices and Their Linear Preservers

Cited by 1 publication

References 21 publications

Jordan triple homomorphisms on $${\mathcal {T}}_\infty (F)$$

Jordan triple homomorphisms on $${\mathcal {T}}_\infty (F)$$

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