The factorization problem in abstract Banach algebras. I. Splitting algebras

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

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Existence of Solutions for an integral equation of Chandrasekhar type in Banach algebras with respect to the weak topology

Operator Theory ◽

10.1515/9783110598193-013 ◽

2021 ◽

pp. 177-182

Author(s):

Amor Fahem ◽

Aref Jeribi ◽

Najib Kaddachi

Keyword(s):

Integral Equation ◽

Weak Topology ◽

Existence Of Solutions ◽

Banach Algebras

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Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem

Discrete Mathematics and Applications ◽

10.1515/dma-2021-0001 ◽

2021 ◽

Vol 31 (1) ◽

pp. 1-4

Author(s):

Mikhail A. Cherepnev

Keyword(s):

Upper Bound ◽

Polynomial Algorithm ◽

Integer Factorization ◽

Factorization Problem ◽

Diffie Hellman ◽

Integer Factorization Problem

Abstract We construct a probabilistic polynomial algorithm that solves the integer factorization problem using an oracle solving the Diffie–Hellman problem.

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COMMUTATIVITY UP TO A FACTOR IN BANACH ALGEBRAS

Demonstratio Mathematica ◽

10.1515/dema-2005-0413 ◽

2005 ◽

Vol 38 (4) ◽

pp. 895-900

Author(s):

Christoph Schmoeger

Keyword(s):

Banach Algebras

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ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972720001392 ◽

2021 ◽

pp. 1-12

Author(s):

PRAKASH A. DABHI ◽

DARSHANA B. LIKHADA

Keyword(s):

Banach Algebra ◽

Banach Algebras ◽

Discrete Groups ◽

Discrete Semigroups ◽

Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

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