The algebra of compact operators does not have any finite-codimensional ideal

Finite Codimensional Invariant Subspace and Uniform Algebra

Finite codimensional invariant subspaces in the abstract Hardy space defined by a unique representing measure on a uniform algebra are described. Mathematics Subject Classification: Primary 47B48

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Generalized Derivation modulo the Ideal of All Compact Operators

The related inequality (1.1) was obtained by Maher [3, Theorem 3.2] who showed that, if A is normal and AT = TA, where T ∈ Cp , then ‖T − (AX −XA)‖p ≥ ‖T‖p for all X ∈ ( ), where Cp is the von Neumann-Schatten class, 1≤ p <∞, and ‖·‖p its norm. Here we show that Maher’s result is also true in the case where Cp is replaced by ( ), the ideal of all compact operators with ‖·‖∞ its norm.Which allow...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

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