Characterizations of Ordered Self-adjoint Operator Spaces

The Laplace operator is essentially self-adjoint

Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...

Characterizations of $L$-convex spaces

In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

Spectral Behaviour of a Simple Non-self-adjoint Operator

We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, where A is a 2 × 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0, 1] ⊂ R. For A ∈ R we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary c...

Spectral properties of unbounded JJ-self-adjoint block operator matrices

We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues. AMS Subject classifi...