Sentence examples for singular numbers from inspiring English sources

In the special case, when the operator ideal L 1,∞) is considered on a type I infinite factor, a bounded operator x belongs to L 1,∞) if and only if the sequence of singular numbers {sn(x)}n⩾1 (in the descending order and counting the multiplicities) satisfies ∥x∥(1,∞)≔supN⩾11Log(1+N)∑n="1Nsn(x)<∞.

In a more extreme example, Latin ī "go!" cumulatively represents in one fused form the verb meaning "go," active voice, imperative mood, second person, and singular number, each a grammatically distinct category.

Peirce is the greatest intellect the Americas ever produced, and it is his whole philosophy, including his semeiotic (note the spelling and the singular number) that now bids fair to prevail as doctrine.

In a barren year artistically, Bangladeshi director Mostofa Sarwar Farooki made a mark with Third Person Singular Number, a stylistically polished and striking drama about a single woman's struggle for an independent life.

See [7, 9] for basic properties and detailed information on the generalized singular number.

Proposition 4.2 includes several generalized singular number inequalities as special cases.

The 'tth singular number (or generalized singular number) of x' (mu _{t}(x)) is defined by mu_{t}(x)=inf bigl{ |xe|: e mbox{ is a projection in } mathcal{M} mbox{ with } tau bigl(e^{bot}bigr)leq t bigr}.

Some related arithmetic-geometric mean and Heinz mean inequalities for a generalized singular number of τ-measurable operators are proved.

As an application of Lemma 3.1 we now obtain the desired generalized singular number inequality (1.3) for τ-measurable operators.

In this article we give some generalized singular number inequalities for products and sums of τ-measurable operators.

The following lemma, which includes a basic property of generalized singular number, plays a central role in our investigation.