ACTA SCIENTIARUM MATHEMATICARUM最新文献

The notion of Cauchy dual for left-invertible covariant representations was studied by Trivedi and Veerabathiran. Using the Moore-Penrose inverse, we extend this notion for the covariant representations having closed range and explore several useful properties. We obtain a Wold-type decomposition for regular completely bounded covariant representation whose Moore-Penrose inverse is regular. Also, we discuss an example related to the non-commutative bilateral weighted shift. We prove that the Cauchy dual of the concave covariant representation ((sigma , V)) modulo (N(widetilde{V})) is hyponormal modulo (N(widetilde{V})).

Let A be a unital Banach algebra with unit e, M be a Banach A-bimodule, and (win A). In this paper, we characterize those continuous linear maps (delta :Arightarrow M) that satisfy one of the following conditions:

for any (a,bin A) with (ab=ba=w), where w is either a separating point with (win Z(A)) or an idempotent.

The concept of weighted numerical radius has been defined recently. In this article, we obtain several upper bounds for the weighted numerical radius of operators and (2 times 2) operator matrices which generalize and improve some well-known famous inequalities for the classical numerical radius. The article also derives an upper bound for the weighted numerical radius of the Aluthge transformation, ({tilde{T}}) of an operator (T in {mathcal {B}}({mathcal {H}}),) where ({tilde{T}} = |T|^{1/2} U |T|^{1/2},) and (T = U |T|) is the Canonical Polar decomposition of T.

M. Lin defined a binary operation for two positive semi-definite matrices in studying certain determinantal inequalities that arise from diffusion tensor imaging. This operation enjoys some interesting properties similar to the operator geometric mean. We study this operation further and present numerous properties emphasizing the relationship with the operator geometric mean. In the end, we present an application toward Tsallis relative operator entropy.

Slim semimodular lattices (for short, SPS lattices) and slim rectangular lattices (for short, SR lattices) were introduced by Grätzer and Knapp (Acta Sci Math (Szeged) 73:445–462, 2007; 75:29–48, 2009). These lattices are necessarily finite and planar, and they have been studied in more then four dozen papers since 2007. They are best understood with the help of their ({mathcal {C}}_1)-diagrams, introduced by the author in 2017. For a diagram F of a finite lattice L and a congruence (alpha ) of L, we define the “quotient diagram” (F/alpha ) by taking the maximal elements of the (alpha )-blocks and preserving their geometric positions. While (F/alpha ) is not even a Hasse diagram in general, we prove that whenever L is an SR lattice and F is a ({mathcal {C}}_1)-diagram of L, then (F/alpha ) is a ({mathcal {C}}_1)-diagram of (L/alpha ), which is an SR lattice or a chain. The class of lattices isomorphic to the congruence lattices of SPS lattices is closed under taking filters. We prove that this class is closed under two more constructions, which are inverses of taking filters in some sense; one of the two respective proofs relies on an inverse of the quotient diagram construction.

We investigate general properties of multipliers and weak multipliers of algebras. We apply the results to determine the (weak) multipliers of associative algebras and zeropotent algebras of dimension 3 over an algebraically closed field.

Hahn (Math Phys 32:3–88, 1922) defined the sequence space h. The main purpose of this study is to introduce the new Hahn sequence space (h(C_{m})) as the domain of Cesàro mean of order m and give some topological properties of the space (h(C_{m})). Moreover, we determine the alpha-, beta- and gamma-duals of the space (h(C_{m})) and characterize the classes ((ell _1:h)), ((h:ell _p)), ((h(C_m):V_{1})) and ((V_{2}:h(C_{m}))) of matrix transformations, where (1<p<infty ), (V_{1}in {ell _{infty },c,c_{0},ell _p}) and (V_{2}) is any given sequence space. Finally, we compute the norm of the operators belonging to ({mathcal {B}}(ell _1,h(C_m))) and determine the Hausdorff measure of noncompactness of the operators in ({mathcal {B}}(ell _1,h(C_m))).

In this paper, we define the wave-packet transform (WPT) involving Lebedev–Skalskaya transform (LS-transform) and establish some norm estimates of LS-wavelet, LS-wavelet transform, and Plancherel’s relation for WPT. Moreover, we obtain the Calderon-type reproducing formula using LS-transform theory and its convolution.