The product of operators with closed range
نویسندگان
چکیده
منابع مشابه
On the decomposable numerical range of operators
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi :Hrightarrow mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{chi}(H)$ the symmetry class of tensors associated with $H$ and $chi$. Let $K(T)in (V_{chi}(H))$ be the operator induced by $Tin text{End}(V)$. Th...
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Denote by W (A) the numerical range of a bounded linear operator A, and [A, B] = AB −BA the Lie product of two operators A and B. Let H, K be complex Hilbert spaces of dimension ≥ 2 and Φ : B(H) → B(K) be a map whose range contains all operators of rank ≤ 1. It is shown that Φ satisfies that W ([Φ(A), Φ(B)]) = W ([A, B]) for any A, B ∈ B(H) if and only if dim H = dim K, there exist ε ∈ {1,−1}, ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1973
ISSN: 0040-8735
DOI: 10.2748/tmj/1178241337