ACTA SCIENTIARUM MATHEMATICARUM最新文献

Let (H(mathbb D)) be the linear space of all analytic functions on the open unit disc (mathbb D) and (H^p(mathbb D)) the Hardy space on (mathbb D). The characterization of complex linear isometries on (mathcal {S}^p={ fin H(mathbb D):f'in H^p(mathbb D) }) was given for (1 le p < infty ) by Novinger and Oberlin in 1985. Here, we characterize surjective, not necessarily linear, isometries on (mathcal {S}^infty ).

Let ({text {Lip}}(I)) be the Banach algebra of all Lipschitz functions on the closed unit interval I with the norm (Vert fVert _L=Vert fVert _infty +L(f)) for (fin {text {Lip}}(I)), where L(f) is the Lipschitz constant of f. We denote by (C^{1}(I, {text {Lip}}(I))) the Banach algebra of all continuously differentiable functions F from I to ({text {Lip}}(I)) equipped with the norm (Vert FVert _{Sigma }=sup _{sin I}Vert F(s)Vert _L+sup _{tin I}Vert D(F)(t)Vert _L) for (Fin C^{1}(I, {text {Lip}}(I))). In this paper, we prove that if T is a surjective, not necessarily linear, isometry on (C^{1}(I, {text {Lip}}(I))), then (T-T(0)) is a weighted composition operator or its complex conjugation. Among other things, any surjective complex linear isometry on (C^{1}(I, {text {Lip}}(I))) is of the following form: (c_{1}F(tau _1(s),tau _2(x))), where (c_{1}) is a complex number of modulus 1, and (tau _1) and (tau _2) are isometries of I onto itself.

Let L be a slim, planar, semimodular lattice (slim means that it does not contain an ({{textsf{M}}}_3)-sublattice). We call the interval (I = [o, i]) of L rectangular, if there are complementary (a, b in I) such that a is to the left of b. We claim that a rectangular interval of a slim rectangular lattice is also a slim rectangular lattice. We will present some applications, including a recent result of G. Czédli. In a paper with E. Knapp about a dozen years ago, we introduced natural diagrams for slim rectangular lattices. Five years later, G. Czédli introduced ({mathcal {C}}_1)-diagrams. We prove that they are the same.

We develop upper and lower bounds for the numerical radius of (2times 2) off-diagonal operator matrices, which generalize and improve on some existing ones. We also show that if A is a bounded linear operator on a complex Hilbert space, then for all (rge 1),

where w(A), (Vert AVert ) and (Re (A)), respectively, stand for the numerical radius, the operator norm and the real part of A. This (for (r=1)) improves on some existing well-known numerical radius inequalities.

The multivariable autoregressive filter problem asks for a polynomial (p(z)=p(z_1, ldots , z_d)) without roots in the closed d-disk based on prescribed Fourier coefficients of its spectral density function (1/|p(z)|^2). The conditions derived in this paper for the construction of a degree one symmetric polynomial reveal a major divide between the case of at most two variables vs. the the case of three or more variables. The latter involves multivariable elliptic functions, while the former (due to [Geronimo and Woerdeman (Ann Math 160(3):839-906, 2004)]) only involve polynomials. The three variable case is treated with more detail, and entails hypergeometric functions. Along the way, we identify a seemingly new relation between ({}_2 F_{1}left( {frac{1}{3},frac{2}{3}atop 1}; zright) ) and ({}_2 F_{1}left( {frac{1}{2},frac{1}{2}atop 1}; widetilde{z}right) ).

In this article, we give a representation of absolutely norm attaining (*)-paranormal operators. More specifically, we prove that every (*)-paranormal absolutely norm attaining operator T can be decomposed as (Uoplus D), where U is a direct sum of scalar multiples of unitary operators and D is an upper triangular block operator matrix. Later, we provide a sufficient condition under which a (*)-paranormal absolutely norm attaining operator is normal.

A Hilbert space operator A is said to be core invertible if it has an inner inverse whose range coincides with the range of A and whose null space coincides with the null space of the adjoint of A. This notion was introduced by Baksalary, Trenkler, Rakić, Dinčić, and Djordjević in the last decade, who also proved that core invertibility is equivalent to group invertibility and that the core and group inverses coincide if and only if A is a so-called EP operator. The present paper contains criteria for core invertibility and for the EP property as well as formulas for the core inverse for operators in the von Neumann algebra generated by two orthogonal projections.

Ampliation quasisimilarity was applied as a tool in Foias and Pearcy (J Funct Anal 219:134–142, 2005) to reduce the hyperinvariant subspace problem to a particular class of operators. The seemingly weaker pluquasisimilarity relation was introduced in Bercovici et al. (Acta Sci Math Szeged 85:681–691, 2019) and studied also in Kérchy (Acta Sci Math Szeged 86:503–520, 2020). The problem whether these two relations are actually equivalent is addressed in the present paper. The following more general, related question is studied in details: under what conditions is the operator A a quasiaffine transform of B, whenever A can be injected into B and A can be also densely mapped into B.

Let H be a complex Hilbert space and let ({mathcal {B}}(H)) be the algebra of all bounded linear operators on H. In this paper, for (Tin {mathcal {B}}(H)) and a unit vector (xin H), we introduce a local version of the reduced minimum modulus of T at x, noted by (gamma (T, x)). Properties of this quantity are investigated. We study the relations between (gamma (T, x)) and the Moore–Penrose inverse, spectrum of (vert Tvert ) and the local spectrum of (vert Tvert ) at x. At the end of this paper we will be interested in several problems around this quantity (preserving, continuity, local spectral theory).

This paper considers discrete and continuous semigroups of (weighted) composition operators on the Fock space. For discrete semigroups consisting of powers of a single operator, the asymptotic behaviour of the semigroups is analysed. For continuous semigroups and groups, a full classification of possible semigroups is given, and the generator is calculated.