This work presents a new and fast algorithm for binary morphological erosions with arbitrary shaped structuring elements inspired by preprocessing techniques that are quite similar to those presented ...in many fast string matching algorithms (jumps and miss-matchings). The result of these preprocessing techniques is a speed up for computing binary erosions. A time complexity analysis shows that this algorithm has clear advantages over some known implementations. Experimental results confirm this analysis and shows that this algorithm has a good performance and can be a better option for erosions computation.
Let A= (A_{1},...,A_{p}) and B=(B_{1},...,B_{p}) denote two p-tuples of operators with A_{i}\in \mathcal L(H) and B_{i}\in \mathcal L(K). Let R_{2,A,B} denote the elementary operators defined on the ...Hilbert-Schmidt class \mathcal C^{2}(H,K) by R_{2,A,B}(X)=A_{1}XB_{1}+...+A_{p}XB_{p}. We show that co\left(W_{e}(A)\circ W(B))\cup (W(A)\circ W_{e}(B))\right\subseteq V_{e}(R_{2,A,B}). Here V_{e}(.) is the essential numerical range, W(.) is the joint numerical range and W_{e}(.) is the joint essential numerical range.
We prove the orthogonality of the range and the kernel of an important class of elementary operators with respect to the unitarily invariant norms associated with norm ideals of operators. This class ...consists of those mappings E:B(H)\to B(H), E(X)=AXB+CXD, where B(H) is the algebra of all bounded Hilbert space operators, and A, B, C, D are normal operators, such that AC=CA, BD=DB and \ker A\cap \ker C=\ker B\cap \ker D=\{0\}. Also we establish that this class is, in a certain sense, the widest class for which such an orthogonality result is valid. Some other related results are also given.
We study spectrally bounded elementary operators of length two on a complex unital Banach algebra A. Some related conditions are investigated as well. In particular, we show that if S is an ...elementary operator of length two such that S(x) is quasi-nilpotent for every x ∈ A, then S(x)3 ∈ radA for every x ∈ A.
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\begin{document}$$\overline{{\rm E}_1({\rm A})}^{p.n.}$$\end{document}be the closure in the point-norm topology of the set of all completely contractive elementary operators on a C* -algebra A. If \documentclass12pt{minimal}
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\begin{document}$$\psi \in \overline{{\rm E}_1({\rm A})}^{p.n.}$$\end{document}. A completely positive contraction on ø a von Neumann algebra R is \documentclass12pt{minimal}
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\begin{document}$$\overline{{\rm E}_1({\rm R})}^{p.n.}$$\end{document} in if and only if the normal and the singular part of ø are both in \documentclass12pt{minimal}
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\begin{document}$$\overline{{\rm E}_1({\rm R})}^{p.n.}$$\end{document}. Maps on R admitting pointwise approximation by sequences of elementary complete contractions may have additional properties that are not shared by all maps in\documentclass12pt{minimal}
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\begin{document}$$\overline{{\rm E}_1({\rm R})}^{p.n.}$$\end{document}. A specific example on B(H) is also studied.
Let 𝔄 be a Banach algebra. The flip on 𝔄 ⊗ 𝔄op is defined through 𝔄 ⊗ 𝔄op ∋ a ⊗ b ↦ b ⊗ a. If 𝔄 is ultraprime, 𝓔ℓ(𝔄), the algebra of all elementary operators on 𝔄, can be algebraically ...identified with 𝔄 ⊗ 𝔄op, so that the flip is well defined on 𝓔ℓ(𝔄). We show that the flip on 𝓔ℓ(𝔄) is discontinuous if 𝔄 = 𝒦(E) for a reflexive Banach space E with the approximation property.
Let R be a von Neumann algebra on a Hilbert space H with commutant R' and centre C. For each subspace Y of R let$\operatorname{ref}_{\mathscr{R}}(\mathscr{Y})$be the space of all B ∈ R such that XBY ...= 0 for all X, Y ∈ R satisfying X Y Y = 0. If$\operatorname{ref}_{\mathscr{R}}(\mathscr{Y}) = \mathscr{Y}$, the space Y is called R-reflexive. (If R = B(H) and Y is an algebra containing the identity operator, R-reflexivity reduces to the usual reflexivity in operator theory.) The main result of the paper is the following: if Y is one-dimensional, or if Y is arbitrary finite-dimensional but R has no central portions of type Infor$n > 1$, then the space$\overline{\mathscr{CY}}$is R-reflexive and the space$\overline{\mathscr{R}'\mathscr{Y}}$is B(H)-reflexive, where the bar denotes the closure in the ultraweak operator topology. If R is a factor, then R'Y is closed in the weak operator topology for each finite-dimensional subspace Y of R.
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