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Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems

Rudolf L. Voller (1992)

Applications of Mathematics

In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.

Alcune osservazioni sul rango numerico per operatori non lineari

Jürgen Appell, G. Conti, Paola Santucci (1999)

Mathematica Bohemica

We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).

Algebra isomorphisms between standard operator algebras

Thomas Tonev, Aaron Luttman (2009)

Studia Mathematica

If X and Y are Banach spaces, then subalgebras ⊂ B(X) and ⊂ B(Y), not necessarily unital nor complete, are called standard operator algebras if they contain all finite rank operators on X and Y respectively. The peripheral spectrum of A ∈ is the set σ π ( A ) = λ ∈ σ ( A ) : | λ | = m a x z ∈ σ ( A ) | z | of spectral values of A of maximum modulus, and a map φ: → is called peripherally-multiplicative if it satisfies the equation σ π ( φ ( A ) ∘ φ ( B ) ) = σ π ( A B ) for all A,B ∈ . We show that any peripherally-multiplicative and surjective map φ: → , neither assumed to be linear nor...

Algebra of multipliers on the space of real analytic functions of one variable

Paweł Domański, Michael Langenbruch (2012)

Studia Mathematica

We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.

Algebraic analysis in structures with the Kaplansky-Jacobson property

D. Przeworska-Rolewicz (2005)

Studia Mathematica

In 1950 N. Jacobson proved that if u is an element of a ring with unit such that u has more than one right inverse, then it has infinitely many right inverses. He also mentioned that I. Kaplansky proved this in another way. Recently, K. P. Shum and Y. Q. Gao gave a new (non-constructive) proof of the Kaplansky-Jacobson theorem for monoids admitting a ring structure. We generalize that theorem to monoids without any ring structure and we show the consequences of the generalized Kaplansky-Jacobson...

Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

Fangyan Lu, Pengtong Li (2003)

Studia Mathematica

It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary...

Algebraic properties of Toeplitz operators on weighted Bergman spaces

Amila Appuhamy (2021)

Czechoslovak Mathematical Journal

We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property and commutative property are discussed. Further we apply our results to solve a compactness problem of the product of two Hankel operators on the weighted Bergman space on the unit bidisk.

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