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Wave front set for positive operators and for positive elements in non-commutative convolution algebras

Joachim Toft (2007)

Studia Mathematica

Let WF⁎ be the wave front set with respect to C , quasi analyticity or analyticity, and let K be the kernel of a positive operator from C to ’. We prove that if ξ ≠ 0 and (x,x,ξ,-ξ) ∉ WF⁎(K), then (x,y,ξ,-η) ∉ WF⁎(K) and (y,x,η,-ξ) ∉ WF⁎(K) for any y,η. We apply this property to positive elements with respect to the weighted convolution u B φ ( x ) = u ( x - y ) φ ( y ) B ( x , y ) d y , where B C is appropriate, and prove that if ( u B φ , φ ) 0 for every φ C and (0,ξ) ∉ WF⁎(u), then (x,ξ) ∉ WF⁎(u) for any x.

Weak multiplicative operators on function algebras without units

Thomas Tonev (2010)

Banach Center Publications

For a function algebra A let ∂A be the Shilov boundary, δA the Choquet boundary, p(A) the set of p-points, and |A| = |f|: f ∈ A. Let X and Y be locally compact Hausdorff spaces and A ⊂ C(X) and B ⊂ C(Y) be dense subalgebras of function algebras without units, such that X = ∂A, Y = ∂B and p(A) = δA, p(B) = δB. We show that if Φ: |A| → |B| is an increasing bijection which is sup-norm-multiplicative, i.e. ||Φ(|f|)Φ(|g|)|| = ||fg||, f,g ∈ A, then there is a homeomorphism ψ: p(B) → p(A) with respect...

Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.

Rajappa K. Asthagiri (1991)

Extracta Mathematicae

In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.

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