Do ng-show="result.resultId.indexOf('One') == 0", etc.

A simple way to do this is to add a new method to your scope.

$scope.startsWith = function (actual, expected) {
    var lowerStr = (actual + "").toLowerCase();
    return lowerStr.indexOf(expected.toLowerCase()) === 0;
}

Then change the filter syntax on your element.

<ul border="1px" ng-repeat="msg in messages | filter:search:startsWith">

Here is a working plunkr with the example above.

Use startsWith method like this

<div *ngIf="name.startsWith('@')">
  Show something
</div>

And if you want to check if string doesn't start with '@' simply add '!' like *ngIf="!name.startsWith('@')"

Adding to what Eliseo has to say, I would also like to correct your existing use of pipe.

<div>{{ name | startsWith : 'Ang' }}</div>

<div *ngIf="( name | startsWith : 'Ang')"> Can see </div>

<div *ngIf="( name | startsWith : 'Test')"> Can't see </div>

Take a look at this demo code here

OR

<app-breadcrumb  *ngIf="(url.startsWith('/register/'))"></app-breadcrumb>

Don't use pipe for such checks, its mostly for data transformation

valueChanges will not emit any values initially (until state actually changes). When you need to calculate something from initial state you use startWith to make observable emit a value even though it wouldn't normally.

If you want to process initial value without startWith, you can create another stream

Observable.of(stateCtrl.value).pipe(
  map(state => state ? this.filterStates(state) : this.states.slice())
);

which will emit only one value. But it's easier to handle both cases at the same time, so startWith is a good way to do it...