Rank α operators on the space C(T,X)

Dumitru Popa

Displaying similar documents to “Rank α operators on the space C(T,X)”

Finite-rank perturbations of positive operators and isometries

Man-Duen Choi, Pei Yuan Wu (2006)

Studia Mathematica

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We completely characterize the ranks of A - B and $A^{1 / 2} - B^{1 / 2}$ for operators A and B on a Hilbert space satisfying A ≥ B ≥ 0. Namely, let l and m be nonnegative integers or infinity. Then l = rank(A - B) and $m = r a n k (A^{1 / 2} - B^{1 / 2})$ for some operators A and B with A ≥ B ≥ 0 on a Hilbert space of dimension n (1 ≤ n ≤ ∞) if and only if l = m = 0 or 0 < l ≤ m ≤ n. In particular, this answers in the negative the question posed by C. Benhida whether for positive operators A and B the finiteness of rank(A - B) implies that...

Rank and perimeter preserver of rank-1 matrices over max algebra

Seok-Zun Song, Kyung-Tae Kang (2003)

Discussiones Mathematicae - General Algebra and Applications

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For a rank-1 matrix $A = a \otimes b^{t}$ over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or $T (A) = U \otimes A^{t} \otimes V$ with some monomial matrices U and V.

Finite rank operators in Jacobson radical $ℛ_{𝒩 \otimes ℳ}$

Zhe Dong (2006)

Czechoslovak Mathematical Journal

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In this paper we investigate finite rank operators in the Jacobson radical $ℛ_{𝒩 \otimes ℳ}$ of $A l g (𝒩 \otimes ℳ)$ , where $𝒩$ , $ℳ$ are nests. Based on the concrete characterizations of rank one operators in $A l g (𝒩 \otimes ℳ)$ and $ℛ_{𝒩 \otimes ℳ}$ , we obtain that each finite rank operator in $ℛ_{𝒩 \otimes ℳ}$ can be written as a finite sum of rank one operators in $ℛ_{𝒩 \otimes ℳ}$ and the weak closure of $ℛ_{𝒩 \otimes ℳ}$ equals $A l g (𝒩 \otimes ℳ)$ if and only if at least one of $𝒩$ , $ℳ$ is continuous.

Opérateurs sur un espace $L^{1}$

Alain Costé, Françoise Lust-Piquard (1987)

Colloquium Mathematicae

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$M_{p}$ -группы с ядром произвольного ранга

В.П. Шунков (1987)

Algebra i Logika

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Rational realization of the minimum ranks of nonnegative sign pattern matrices

Wei Fang, Wei Gao, Yubin Gao, Fei Gong, Guangming Jing, Zhongshan Li, Yan Ling Shao, Lihua Zhang (2016)

Czechoslovak Mathematical Journal

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A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set ${+, -, 0}$ ( ${+, 0}$ , respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix $𝒜$ is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of $𝒜$ . Using a correspondence between sign patterns with minimum rank $r \geq 2$ and point-hyperplane configurations in $ℝ^{r - 1}$ and Steinitz’s theorem on the rational realizability...

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that $rank (P^{*} A Q) = rank (P^{*} A) + rank (A Q) - rank (A),$ where $A$ is idempotent, $[P, Q]$ has full row rank and $P^{*} Q = 0$ . Some applications of the rank formula to generalized inverses of matrices are also presented.

Infinite rank of elliptic curves over $ℚ^{a b}$

Bo-Hae Im, Michael Larsen (2013)

Acta Arithmetica

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If E is an elliptic curve defined over a quadratic field K, and the j-invariant of E is not 0 or 1728, then $E (ℚ^{a b})$ has infinite rank. If E is an elliptic curve in Legendre form, y² = x(x-1)(x-λ), where ℚ(λ) is a cubic field, then $E (K ℚ^{a b})$ has infinite rank. If λ ∈ K has a minimal polynomial P(x) of degree 4 and v² = P(u) is an elliptic curve of positive rank over ℚ, we prove that y² = x(x-1)(x-λ) has infinite rank over $K ℚ^{a b}$ .

Perimeter preserver of matrices over semifields

Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)

Czechoslovak Mathematical Journal

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For a rank- $1$ matrix $A = {𝐚 𝐛}^{t}$ , we define the perimeter of $A$ as the number of nonzero entries in both $𝐚$ and $𝐛$ . We characterize the linear operators which preserve the rank and perimeter of rank- $1$ matrices over semifields. That is, a linear operator $T$ preserves the rank and perimeter of rank- $1$ matrices over semifields if and only if it has the form $T (A) = U A V$ , or $T (A) = U A^{t} V$ with some invertible matrices U and V.

M₂-rank differences for overpartitions

Jeremy Lovejoy, Robert Osburn (2010)

Acta Arithmetica

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