On the Symbols of Strictly m-Null Elementary Operators - Isabel Marrero (Mathematics)
This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is <semantics>(p+q−1)</semantics>-null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly <semantics>(p+q−1)</semantics>-null, then a scalar <semantics>λ≠0</semantics> exists such that <semantics>λA</semantics> is strictly p-null and <semantics>λ−1B</semantics> is strictly q-null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m-isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m-isometries and are subsumed by m-null operators, the result is new.