Resolvent and logarithmic residues of a singular operator pencil in Hilbert spaces

نویسندگان

چکیده

The present paper considers the operator pencil A ( λ ) = 0 + 1 , where ≠ are bounded linear mappings between complex Hilbert spaces and is neither one-to-one nor onto. Assuming that an isolated singularity of image closed, certain operators defined recursively starting from they shown to provide a characterization null space in principal part resolvent logarithmic residues at 0. relations with classical results based on ascent descent [10] discussed. In special case being Fredholm index 0, characterize rank resolvent, dimension subspaces define descent, partial multiplicities, algebraic multiplicity

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ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2022

ISSN: ['1873-1856', '0024-3795']

DOI: https://doi.org/10.1016/j.laa.2022.01.013