c-Numerical radius isometries on matrix algebras and triangular matrix algebras
نویسندگان
چکیده
منابع مشابه
Isometries Between Matrix Algebras
As an attempt to understand linear isometries between C∗-algebras without the surjectivity assumption, we study linear isometries between matrix algebras. Denote by Mm the algebra of m×m complex matrices. If k ≥ n and φ : Mn → Mk has the form X 7→ U [X ⊕ f(X)]V or X 7→ U [X t ⊕ f(X)]V for some unitary U, V ∈ Mk and contractive linear map f : Mn → Mk, then ‖φ(X)‖ = ‖X‖ for all X ∈ Mn. We prove t...
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A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and RMS is an SR-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM), where DM = Homk(M, k) is the dual of M , ...
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Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...
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In 1955, H. Dye defined certain projections of a C∗-matrix algebra by Pi,j(a) = (1 + aa ∗)−1 ⊗ Ei,i + (1 + aa∗)−1a⊗ Ei,j + a∗(1 + aa∗)−1 ⊗ Ej,i + a∗(1 + aa∗)−1a⊗ Ej,j , which was used to show that in the case of factors not of type I2n, the unitary group determines the algebraic type of that factor. We study these projections and we show that in M2(C), the set of such projections includes all t...
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We show how the data of a finite dimensional weak C∗-Hopf algebra can be encoded into a pair (H, V ) where H is a finite dimensional Hilbert space and V :H⊗H → H⊗H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudomultiplicative unitary approac...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.10.012