When the Banach algebra A is the algebra L ( X ) of bounded linear operators on a complex Banach space X ( e. g., the algebra of square matrices ), the notion of the spectrum in A coincides with the usual one in the operator theory.

When many partially transparent layers need to be composited together, it is worthwhile to consider the algebraic properties of compositing operators used.

When the servers merge, any pre-existing operators retain their status, allowing the new user to kick out the original operators and take over the channel.

When the Russian economy ’ s collapse came about in August 1998, the market shrank drastically and the ruble fell several cellular operators were squeezed between low traffic and huge foreign currency denominated credits and telecommunications equipment bills.

When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated here:

When the system S is prepared in a pure state, it is associated with a vector in H. Measurable quantities are associated with Hermitian operators acting on H: these are referred to as observables.

When everything was operating correctly this was true, and the operators became habituated to rely on it.

When manual switching systems began to be replaced by automatic, or " dial " systems, there was frequently concern among users that the very personalized emergency service provided by manual operators would be lost.

When the above hold, quantum theory can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the Hamiltonian.

When the paddle is pressed to the left it makes a continuous contact suitable for sending dashes ( or dahs, as most operators call them ).

When the Avro 504s, Bristol F. 2 Fighters and, De Havilland designed, Airco DH. 4s and Airco DH. 9s did reach New Zealand they were either placed in storage or loaned to the flying schools, barnstormers and nascent commercial operators.

When the team was founded, HRT operators used the 9mm FN-Browning Hi-Power Mk 2 pistol, which was later supplemented by the 9mm SIG P226 pistol.

When these machines were in heavy use, it was not uncommon for an operator to set type at the rate of over 4, 000 ems per hour ( the fastest operators being able to exceed 10, 000 ems per hour ) so the need for careful lubrication and regular cleaning was essential to keep these machines operating at their full potential.

When the dimension of H is infinite, then S < sub > 1 </ sub >( H ) ( the trace class ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup > 1 </ sup >, and S < sub >∞</ sub >( H ) = L ( H ) ( the bounded operators ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup >∞</ sup > ( in both cases, the subspace can be chosen to be the operators diagonal with respect to a given orthonormal basis of H ).

When operators are developing flight plans for their aircraft, the PBN approach encourages them to assess the overall accuracy, integrity, availability, continuity and functionality of the aggregate navigation aids present within the applicable airspace.

When the Chiltern Railways services are included, Amersham still has four trains an hour to London in total, with extra trains from both operators in the peak.

When the knob is pressed from the right, it makes a continuous contact suitable for sending dashes ( or dahs, as most operators call them ).

When so activated, the Radio Amateur Civil Emergency Service will consist of only those amateur radio operators who have previously registered with State and local governments to provide emergency radio communications for them in times of emergency.

When more than one associative prefix or postfix operator of equal precedence precedes or succeeds an operand, the operators closer to the operand associate first.

When prefix and postfix operators of equal precedence coexist, the order of association is undefined.

When considering hyper operators, the term hyper refers to all ranks, and the term super refers to rank 4, or tetration.

When a captured German revealed under interrogation that Enigma operators had been instructed to encode numbers by spelling them out, Alan Turing reviewed decrypted messages and determined that the number “ eins ” (" 1 ") was the commonest string in the plaintext.

When they were closer and he saw that one was a woman, he was more puzzled than ever.

When they were finally satisfied, Jones said, `` I think he's going to give us work ''.

When they were ready to leave, Benson and Ramey walked back around the rear of the trailer.

When they reached the school, a gang of boys and girls were already there playing `` crack the whip '' in front of the schoolhouse.

When these had been pocketed, we could still spend a morning cracking open other pebbles for our delight in seeing how much prettier they were inside than their dull exteriors indicated.

When he discovered they had received from the Company's Court of Directors no permission to live in India, coupled with the fact that they were Americans who had been sent to Asia to convert `` the heathen '', he became more belligerent than ever.

When Prudence and Blackberry were too young to be trusted in the dining room, they were tied to the radiator with their leashes, and they would cry.

When they were first written, there was evidently no thought of their being published, and those which refer to the writer's love for Mrs. Meynell particularly have the ring of truth.

When their levies came shambling into camp, they were all elbows, hair, and beard.

When, in March, 1640, the two towns were united under Coddington, Gorton claimed the union was irregular and illegally constituted and that it had never been sanctioned by the majority of freeholders.

When the negotiations began, his quarrel with the king of France was temporarily in abeyance, and he had no intention of reviving it so long as there was hope that French money would come to pay the troops who, under Charles of Valois, the papal vicar of Tuscany, were so valuable in the crusade against the Colonna cardinals and their Sicilian allies.

When these chores were finished, only then, was she allowed whatever freedom she could find.

When Sir Edward Greville enclosed the town commons on the Bancroft, Quiney and others leveled his hedges on January 21, 1600/1, and were charged with riot by Sir Edward.

When it was over, eight of his company were still alive and all eight were wounded.

When the stock exchange opened this morning, many dealers were quick to purchase shares in Douglas, Lockheed and United Aircraft and prices rose substantially.

When the end did come, and the schools were disbanded and abandoned, we felt and hoped that the machinery of psychological warfare would not be allowed to rust.

When we got there, Trig and the Negro were quarreling over possession of a gold crucifix around the neck of a wounded Filipino.

When it was proposed to rebuild the church, Wilson found that the terms for a new mortgage were very high.

When something unexpected happened, one always asked for water if one were a woman, brandy if one were a man.

When Papa's slender fingers removed the spectacles, there were red indentations on the bridge of the strong nose.

When the telephone rang on the day after Hino went down to the village, Rector had a hunch it would be Hino with some morsel of information too important to wait until his return, for there were few telephones in the village and the phone in Rector's office rarely rang unless it was important.

When values of temperature derived with this instrument were compared with the accepted values associated with liquid helium-4 vapor pressures, differences of about 10 and 7 millidegrees respectively were found.