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A remark concerning Putinar's model of hyponormal weighted shifts

Vasile Lauric (2018)

Czechoslovak Mathematical Journal

The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.

A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.

Karel Horák, Vladimír Müller, Pavla Vrbová (1987)

Aplikace matematiky

The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.

A Remark on a Class of Linear Monotone Operators.

Peter Hess (1972)

Mathematische Zeitschrift

A remark on Berezanskiĭ version on spectral theorem

K. Maurin (1970)

Studia Mathematica

A remark on $C D_{0} (K)$ -spaces.

Alpay, Safak, Ercan, Zafer (2006)

Sibirskij Matematicheskij Zhurnal

A remark on extrapolation of rearrangement operators on dyadic $H^{s}$ , 0 < s ≤ 1

Stefan Geiss, Paul F. X. Müller, Veronika Pillwein (2005)

Studia Mathematica

For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$ , 0 < s < 2, to be the linear extension of the map $(h_{I}) / {(| I |}^{1 / s}) \mapsto (h_{τ (I)}) (| τ (I) |^{1 / s})$ , where $h_{I}$ denotes the $L^{\infty}$ -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s ₀}$ is bounded on $H^{s ₀}$ , then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$ .

A remark on Fefferman-Stein's inequalities.

Y. Rakotondratsimba (1998)

Collectanea Mathematica

It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.