121471662
Alternative proofs of a theorem of Moyls and Marcus on the numerical range of a square matrix
Moyls and Marcus [4] showed that for n⩽4,n×n an complex matrix A is normal if and only if the numerical range of A is the convex hull of the eigenvalues of A. When n⩾5, there exist matrices which are not normal, but such that the numerical range is still the convex hull of the eigenvalues. Two alternative proofs of this fact are given. One proof uses the known structure of the numerical range of a 2×2 matrix. The other relies on a theorem of Motzkin and Taussky stating that a pair of Hermitian matrices with property L must commute.
122924586
Simultaneous block triangularization and block diagonalization of sets of matrices
Abstract We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of the largest block to polynomial identities. This is used to yield a new proof of a theorem of Watters [20] which gives a necessary and sufficient condition for a set of matrices to be simultaneously, unitarily similar to block diagonal matrices with blocks of sizes one or two.
35563801
INTEGRATION OVER HILBERT SPACE AND OUTER EXTENSIONS.
116997880
A counterexample in harmonic analysis
123488492
SOME REMARKS ON WEIGHTED POLYNOMIAL APPROXIMATIONS OF HOLOMORPHIC FUNCTIONS
Production of oxidation resistant, thermal shock resistant and high strength composites, produced by hot pressing at high temperatures, e.g., about 2,100 DEG C, a mixture preferably of a boride such as hafnium diboride, a silicide such as tungsten disilicide, and a minor portion of discrete carbon particles such as graphite, e.g., a mixture of 66 percent hafnium diboride, 20 percent tungsten disilicide and 14 percent graphite fibers, by weight, against a high temperature resistant substrate, e.g., a metal such as tantalum, to form an integral bonded composite coating on said substrate.
118537421
The modulus of continuity of an analytic function