For a Gaussian measure on a separable Hilbert space with covariance operator C, we show that the family of conditional measures associated with conditioning on a closed subspace S are Gaussian with covariance operator the short S(C) of the operator C to S. We provide two proofs. The first uses the theory of Gaussian Hilbert spaces and a characterization of the shorted operator by Andersen and T...

This paper studies trace class perturbation of closed linear relations in Hilbert spaces. The concept is introduced by orthogonal projections. Equivalent characterizations compact and block operator matrices are first given terms their elements, separately. By using them, several equivalent sufficient obtained.

An important veriication problem for concurrent systems in general is that of establishing whether one system is a correct implementation, or reenement, of another system. For untimed systems, trace inclusion (or variants such as failure inclusion) is often used as a criterion of reenement. The natural extension of this criterion to timed systems is timed trace{inclusion. Unfortunately, this pr...

In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel ...

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trac...

We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten operators is simultaneously triangularizable.

We study the trace class perturbations of half-line, discrete Laplacian and obtain a new bound for perturbation determinant corresponding non-self-adjoint Jacobi operator. Based on this bound, we Lieb–Thirring inequalities such operators. The spectral enclosure spectrum embedded eigenvalues are also discussed.

‎let $v$ be an $n$-dimensional complex inner product space‎. ‎suppose‎ ‎$h$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎hrightarrow mathbb{c} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎denote by $v_{chi}(h)$ the symmetry class‎ ‎of tensors associated with $h$ and $chi$‎. ‎let $k(t)in‎ (v_{chi}(h))$ be the operator induced by $tin‎ ‎text{end}(v)$‎. ‎the...

For the integrable case of the discrete self-trapping (DST) model we construct a Bäcklund transformation. The dual Lax matrix and the corresponding dual Bäcklund transformation are also found and studied. The quantum analog of the Bäcklund transformation (Q-operator) is constructed as the trace of a monodromy matrix with an infinite-dimensional auxiliary space. We present the Q-operator as an e...