Note on singular perturbation of linear operators

A Note on Perturbation Theory for Semi-groups of Operators

1. I. S. Cohen, Commutative rings with restricted minimum conditions, Duke Math. J. 17 (1950), 27-41. 2. S. MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771-782. 3. N. Nakano, Idealtheorie in einem speziellen unendlichen algebraischen Zahlkorper, J. Sei. Hiroshima Univ. 16(1953), 425-439. 4. O. Zariski and P. Samuel, Commutative a...

on the effect of linear & non-linear texts on students comprehension and recalling

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A Note on Perturbation Results for Learning Empirical Operators

A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a similarity function or a kernel, given empirical data. Thus for the analysis of algorithms, it is an important problem to be able to assess the quality of such approximations. The ...

A Note on Calderón-zygmund Singular Integral Convolution Operators

A Note on James Spaces and Superstrictly Singular Operators

An elementary lemma is used in order to show that the natural inclusion Jp → Jq of James spaces is superstrictly singular for p < q. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular.