Is it possible to give a more precise formulation of the criterion of maximal accretivity for one extension of nonnegative operator?

The conditions being necessary and sufficient for maximal accretivity and maximal nonnegativity of some closed linear operators in Hilbert space are announced. The following problem is proposed: write down these conditions in more convenient form (one of the admissible variants is indicated).

A general version of Neubauer’s lemma and closed range almost closed operators

In this paper, almost closed subspaces and almost closed linear operators are described in a Hilbert space. We show Neubauer’s lemma and we give necessary and sufficient conditions for an almost closed operator to be with closed range and we exhibit sufficient conditions under which it is either closed or closable.

Well-posedness of fractional degenerate differential equations in Banach spaces

We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and $\begin{array}{} B_{p,q}^s \end{array}$-well-posedness of above equation.

Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces

We give necessary and sufficient conditions of the Lp-well-posedness (resp. -wellposedness) for the second order degenerate differential equation with finite delayswith periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′ (0) = (Mu)′ (2π), where A, B, and M are closed linear operators on a complex Banach space X satisfying D(A) ∩ D(B) ⊂ D(M), F and G are bounded linear operators from into X.

Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces

In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$-well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$, ($t\in \mathbb{R}$), where $A,B$ are closed linear operators on a Banach space $X$ such that $D(A)\subset D(B)$, $a\in \mathbb{C}$ and $0<\unicode[STIX]{x1D6FC}<1$.

Spectral Theory and Differential Operators

This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions. After the exposition of the abstract theory in the first four chapters, Sobolev spaces are introduced and their main properties established. The remaining seven chapters are largely concerned with second-order elliptic differential operators and related boundary-value problems. Particular attention is paid to the spectrum of the Schrödinger operator. Its original form contains material of lasting importance that is relatively unaffected by advances in the theory since 1987, when the book was first published. The present edition differs from the old by virtue of the correction of minor errors and improvements of various proofs. In addition, it contains Notes at the ends of most chapters, intended to give the reader some idea of recent developments together with additional references that enable more detailed accounts to be accessed.

Hölder Continuous Solutions of Degenerate Differential Equations with Finite Delay

Using known operator-valued Fourier multiplier results on vector-valued Hölder continuous function spaces Cα(ℝ; X), we completely characterize the Cα-well-posedness of the first order degenerate differential equations with finite delay (Mu)′(t) = Au(t) + Fut + f(t) for t ∊ ℝ by the boundedness of the (M, F)-resolvent of A under suitable assumption on the delay operator F, where A, M are closed linear operators on a Banach space X satisfying D(A) İ D(M) ≠ = ﹛0﹜, the delay operator F is a bounded linear operator from C([−r, 0]; X) to X, and r > 0 is fixed.

A note on the Hyers-Ulam stability constants of closed linear operators

This paper concerns the properties of the Hyers-Ulam stability constant of closed linear operators. Using the Moore-Penrose inverse, we prove that the mapping T ? KT is lower semi-continuous and give some sufficient and necessary conditions for T ? KT to be continuous or locally bounded.