86 research outputs found
A distance formula related to a family of projections orthogonal to their symmetries
Let u be a hermitian involution, and e an orthogonal projection, acting on
the same Hilbert space. We establish the exact formula, in terms of the norm of
eue, for the distance from e to the set of all orthogonal projections q from
the algebra generated by e,u, and such that quq=0.Comment: 6 pages, 1 figur
Line Segments on the Boundary of the Numerical Ranges of Some Tridiagonal Matrices
Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described
On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces
Let be a semi-almost periodic matrix function with the almost periodic
representatives and at and , respectively.
Suppose is a slowly oscillating exponent such that
the Cauchy singular integral operator is bounded on the variable Lebesgue
space . We prove that if the operator with
and is Fredholm on the variable Lebesgue space
, then the operators and are
invertible on standard Lebesgue spaces and
with some exponents and lying in the
segments between the lower and the upper limits of at and
, respectively.Comment: 23 pages. An inaccuracy in Lemma 3.11 is corrected. The proof of the
main result is corrected accordingl
The possible shapes of numerical ranges
Which convex subsets of the complex plane are the numerical range W(A of some
matrix A? This paper gives a precise characterization of these sets. In
addition to this we show that for any A there exists a symmetric matrix B of
the same size such that W(A)=W(B).Comment: 4 page
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